Where is there a discussion about a rabbinic or halacha-based relief offered to agunot?
There appears to be none mentioned here at Mi Yodea. Correct me, if am wrong. Please include sources, for my learning.
The "old-fashioned" agunah was one where the husband disappeared at sea or the like, and there's insufficient proof of death. As hazoriz mentioned, the Talmud allowed for weaker forms of proof than we might otherwise require, to make it easier for her to remarry. (Still, the rabbis have to be solidly convinced that the husband actually died.) Such questions came up with the sinking of the Titanic, and most recently, on 9/11/2001 with the collapse of the Twin Towers. Rabbi Jachter has an article on that one here; Rabbi Mordechai Willig in New York corresponded with Rav Ovadya Yosef zt'l on some of these questions. Hacham Ovadya wrote some similar responsa about Israeli soldiers who went missing in action.
Next comes the case where the husband's sanity is questionable. A rabbi will make the best attempt they can to make a determination on this; Rabbi Moshe Feinstein had to deal with a guy who claimed he was the Mashiach and sometimes walked around naked; he spent hours and hours trying to: a.) determine whether the fellow was sane enough to give a Get b.) convince the fellow to then do so, at which point he immediately handled the Get there in Liuban, even though normally they preferred to go to a bigger city with more of a history of doing Gittin. The Beth Din of America had the sad case of a husband diagnosed with very aggressive Alzheimer's; they said he should give a Get while he still had the mental capacity to do so.
The third case -- and the most common one today -- is where the husband is alive and well, but chooses not to give a Get. Theoretically, in some cases a Bet Din can order "coercion" against him, and the Mishna even talks about beating him up. (We then use a very creative reading of what's called "giving the Get of his own free will!") In Israel today, if the Bet Din has found "coercion" to be called for (and perhaps some batei din could be more courageous about making this decision), the Israeli government can take away the man's passport, driver's license, and ability to hold a bank account. One time he was already in jail, and they took away his television!
In America, the community can and will protest outside the fellow's house and business and otherwise shun him, which American law allows them to do. American law does not allow them to beat up the fellow, so please don't do that. (One rabbi was recently caught by the FBI for this and sent to jail.)
In both England and New York State, rabbis have successfully lobbied to change the law so that the secular courts will not issue a civil divorce until a Get has been given. (There are some fine details, but that's the basic idea.)
Many other options have been considered over the years; for instance, we could pull aside the groom five minutes after the wedding, ask him to write a Get, and then order the rabbi to deliver it to his wife whenever they're no longer happily together. But the best system, emotionally, is what the Torah describes -- if the marriage falls apart, then he does the right thing and gives her a Get.
Really one of the best options right now is the increased push for an agreement before the couple gets married; these create all sorts of strong incentives for him to give a Get when and if it is called for. Many rabbis have worked very hard on formulating these, defending them halachically, and pushing for them to be used. And if a woman asks for this before the wedding and her fiance refuses to sign it, that's a big warning sign and she should probably think again about marrying him. The most common one in the US is known as "The Beth Din of America prenup" (sometimes called "Rabbi Willig's prenup"); rabbis who belong to the Rabbinical Council of America are required to use one of these when performing a wedding. There's plenty of discussion about it on this website. So far, the BDA prenup has worked every time: if the couple signed one before getting married, then when they got divorced, he has given a Get. There are other forms of agreements, some intended specifically for Israel, as well; though I don't know a lot about their details.
see end of chapter 13 in rambam gittin
The last halacha below sums up the answer
7 If an epidemic was raging throughout the world, and [a woman] says, "My husband died," her word is accepted. For [there is no widely accepted likelihood] with regard to a plague; everyone knows that in a time of plague some die and some live. And it is possible that strong young men will die from the plague, and elderly infirm people will be saved. And therefore, we do not suspect that she relied on the likelihood that most people died.
8 It has already been stated that a witness who [did not see evidence of the person's death himself, but who] testifies after hearing the statements of another person is acceptable with regard to [the verification of the death of] a woman's [husband].
When does this apply? When the person heard a mentally competent adult - even a servant or a maid -servant - say that so and so died. If, however, a person heard from a mentally incompetent person or from a minor that an individual died, he may not testify [to that effect], nor do we rely on their statements.
9 [There is an exception to the above principle.] If a person heard children saying: "We just came from so and so's funeral. These and these many people recited eulogies. The sage so and so and these and these others followed the bier. A nd this and this is what happened to the bier," the person may offer this as testimony [regarding a man's death], and on this basis permission is granted for [the deceased's] wife to remarry.
10 When a Jew says, "I killed so and so," [the man's wife] is allowed to remarry on the basis of his testimony. [The rationale is] a person's own testimony cannot be used to incriminate him. [Therefore, he is not disqualified, and] he did testify that [the husband] died.
11 It has already been stated that statements made by a gentile in the course of conversation can be used as a basis to grant [a woman] permission to remarry.
What is implied? If a gentile exclaimed: "How terrible is it that so and so died! He was so nice! He did so much for me!" Or if the gentile was talking and said, "We were traveling on our way, and to our amazement, so and so who was traveling with us fell down and died. We all were amazed that he died so suddenly." If he makes statements of this nature that indicate that he has no intention of giving testimony, his word is accepted.
12 When a Jew hears a gentile [say] in the course of conversation [that a man died], he may testify that he heard these statements, and the man's wife may be granted permission to remarry on this basis.
When does the above apply? When there is no rationale to explain [why the gentile would make these statements if they were not true]. If, however, there could be a reason for the gentile's statements, and he is making them with another intent in mind [his word is not accepted].
For example, [a gentile] told a Jew, "Do such and such for me, or else I will kill you, as I killed so and so," he is not making these statements in the course of conversation, for his intent is to cast fear upon his listener.
13 Similarly, if a person heard the gentile legal authorities say, "We executed so and so," their word is not accepted. For they will use falsehood to reinforce their position and to cast fear [among the populace]. The same applies in all similar instances.
14 When, at first, a gentile made statements in the course of conversation, and afterwards was asked questions [by Jews] until all the details [of the person's death] were disclosed, his statements are accepted, and the woman is granted permission to remarry on this basis.
15 It has already been stated that a witness who testifies: "I heard that so and so died," is acceptable with regard to testimony [concerning] a woman's [husband], and the woman may remarry on this basis. [This applies even when] he heard the statements from a woman or from a servant.
If, however, a witness, a woman or a servant says: "So and so died; I saw that he died," the witness should be asked: "What did you see? How do you know that he died? " If the witness responds with clear [testimony], his word is accepted. If the witness replies, describing a situation in which it is highly likely that the person would have died, we do not grant his wife license to remarry. For testimony concerning a man's death [can be accepted] only when [the witness can say] with certainty that he saw the man die, and there is no doubt concerning the matter.
16 What is implied? If a man was seen falling into the sea, even if he fell into the ocean, testimony should not be offered that the man died, because it is possible that he was cast away or escaped [from the sea] from an [unseen] place.
If he fell into a body of water with definite boundaries - e.g., a cistern or a cavern in which a person standing [at the edge] could see the entire periphery - testimony that the man died may be offered, and license may be granted for his wife to remarry, provided [the witnesses] remained there for a period of time beyond which it was impossible for the man to live, and saw that he did not ascend [from the body of water].
Similarly, if he was cast into the sea and a net was cast in after him, and a limb that a person would not be able to live without was raised up, testimony may be offered that he died, and his wife may [be granted license] to remarry.
17 If [a man] fell into a lair of lions, leopards or the like, testimony that he died may not be offered, for it is possible that they will not eat him. If he fell into a pit of snakes and scorpions, into a furnace, or into a boiling caldron filled with wine or oil, or his esophagus and windpipe were slit - either in their majority or in their entirety - testimony may be offered that he died, even if he arose and fled. For [in these situations], he ultimately will die.
Similar laws apply in all situations in which it is impossible that the person will live, but rather will die shortly afterwards. Testimony may be offered that he [died].
18 If we see a man hanging and a vulture eating from his body, testimony may not be offered that he died. [This applies] even if he was stabbed with a lance, or arrows were shot at him.
If, however, we see the vulture eating from a place that would cause him to die - e.g., his brain, his heart or his intestines, one may offer testimony that he died.
19 [The following laws apply when] one witness testifies, "I saw that he died in a war or in a landslide, or that he drowned in the ocean and died," or mentioned other causes that would probably lead to death. If he says, "I buried him," his statements are accepted, and she may be granted permission to remarry. If he did not say, "I buried him," she should not be granted permission to remarry. If, however, she remarries, she need not leave [her second husband].
20 Similarly, if one witness testifies that a woman's husband drowned in the sea or in a body of water that does not have a defined periphery, he did not emerge [from the water], all traces of him have disappeared, and his existence has been forgotten, the woman should not [be granted license to] remarry on this basis, as we have explained.
If, however, she remarries, she need not be forced to leave her second husband. Even if a gentile said in the course of conversation, "So and so drowned at sea," and on this basis [the man's wife] remarried, she need not be forced to leave her second husband. Nevertheless, [in the above instances,] the sage who gave permission for her to remarry should be placed under a ban of ostracism.
21 [The following rules apply when the body of a man who was] slain or died of natural causes is discovered. If his forehead, his nose and his facial features are intact, and his identity can be established based on them, testimony concerning his death may be offered.
If, however, any of these identifying factors is missing, even if there are signs [through which he can be identified] on his body and on his personal artifacts, even if one of those signs is a mole, testimony concerning his death should not be offered.
When does [the leniency mentioned in the first clause] apply? When the corpse was seen within three days of his murder or death. After three days have passed, testimony concerning his death should not be offered, because his facial features [may have] become distorted.
22 [The following rules apply when a man] drowned at sea and was cast out onto dry land. Although several days have passed, if his facial features and his nose can be identified, testimony may be offered with regard to his [death], for in water the features of a corpse do not become distorted until an extremely long period of time has passed.
If the corpse lay on dry land for twelve hours after being cast out of the sea and the corpse became bloated, testimony may not be offered because [his features] have been distorted. When we look at the form [of a corpse] in order to identify [a man] to offer testimony with regard to his [death], [it is acceptable if] we look at [the corpse] even by candlelight or by moonlight.
23 [The following rule applies when] we see a person at a distance and he says that he is so and so, the son of so and so, or so and so from a particular place, and that he has been bitten by a snake and is dying. Even if we go [to the place where he was standing], find [the corpse and discover] that its features have changed to the extent that it is no longer distinguishable, we may, nevertheless, [grant license for] his wife [to] remarry:
24 [A person's testimony is effective in the following instance.] A person came and said: "A court - or people - told me, when you arrive at this and this place, tell them that Yitzchak, the son of Michael, died." When this person came to that place and delivered the message - although he is not aware of the identity [of the deceased] - since [the people at that place] do know his identity, [the deceased's] wife [may be granted] permission [to remarry]. We do not presume that perhaps it was another person named Yitzchak, the son of Michael, who died.
25 When a Jew and a gentile left from our [location] for a different destination, and the gentile came and said in the course of conversation: "The man who left [this city] with me died," [the deceased's] wife [may be granted license to] remarry. [This applies] even when the gentile does not know the identity of the man, provided he says: "I buried him."
26 Similarly, when ten men were taken together while shackled in chains or tied by heavy ropes used to lead camels or the like, from one place to another, and a gentile came and said in the course of conversation that all ten men who went out while tied died, and he buried them, their wives [may be granted license to] remarry.
27 If a Jew says: "A Jewish man died in our company in this and this place. These and these were his facial features. These and these were signs of identification," we do not make a guess and say that it was probably so and so. Rather [the person is not considered to have died] until a witness mentions his name and the name of his city.
If, however, [a person] says: "One of the inhabitants of the city of so and so journeyed out in our company and died," we check in that city. If only one man left the city, his wife [may be given permission to] marry.
28 [The following rule applies if] a document was found saying: "So and so, the son of so and so, died," or "So and so, the son of so and so, was killed": If it can be determined that this was written by a Jew, [the man's] wife [may be given permission to] marry.
Similarly, when a person has lost the power of speech, and he was tested, as he would be tested with regard to a get, and it is proven that he is mentally sound, if he writes that so and so died, we may rely on his writing, and [the deceased's] wife [may be given permission to] marry.
We do not follow the standard process of interrogation with regard to witnesses who testify [concerning the death of] a woman's [husband]. For our Sages did not speak about establishing stringencies regarding such matters. [Indeed, their approach was characterized by] leniency in order to permit a woman without a husband [to remarry].
29 Do not wonder at the fact that our Sages discharged the prohibition [against a married woman], which is considered a very severe matter, on the basis of the testimony of a woman, a servant or a maidservant, statements made by a gentile in the course of conversation, a written statement or [testimony] that was not investigated by the ordinary process of interrogation, as we have explained. [These leniencies were instituted] because the Torah requires only testimony of two witnesses, and all the other details of the laws of witnesses with regard to matters that cannot be verified definitively except via witnesses and their testimony - e.g., that one person killed another, or that one person lent money to another. When, by contrast, the matter may be verified definitively without the testimony of a witness, and the witness cannot justify [his statements] if they are not true - e.g, when one testifies that a person died, the Torah did not necessitate [that the requirements of formal testimony be met in these instances]. For it is unlikely that a witness will testify falsely. For this reason, our Sages [extended] the leniency with regard to this matter and accepted the testimony of a single witness that is based on the testimony of a maidservant, [testimony] from a written document, and [testimony] that was not investigated by the ordinary process of interrogation. [These leniencies were accepted] so that the daughters of Israel will not be forced to remain unmarried.