Is there an idea of Beit Din unlawfully pardoning, as opposed to unlawfully killing?

Question

A Jewish Court is allowed to kill a person if it considers the killing worthy even if it is unlawful by the existing Jewish Halacha. This is called עונשין שלא מן הדין (Meggilat Taanit 86, also Sanhedrin 46a and Rambam Sanhedrin 24,4):

אמר רבי אליעזר בן יעקב שמעתי שב"ד מלקין והורגין שלא מן התורה. דבית לוי אמרו שמעתי שב"ד עונשין ממון ומכים שלא מן התורה. לא מפני שכתוב בתורה אלא משום שנאמר ובערת הרע מקרבך...
שוב מעשה באחד שרכב על הסוס בשבת והביאוהו לב"ד וסקלוהו וכי חייב היה אלא שהיתה השעה צריכה לכך כדי שילמדו אחרים:

As we see a person was killed just because the court thought it was a good idea to teach others, not because of the magnitude of his own sin.

As a Baal Teshuva (a newcomer to Judaism) I would assume exactly the opposite - that the court would be allowed to unlawfully minimize or skip the punishment altogether if they see a need:

1. Because we value life so much (needless to source) and we're so Rachmanim sons of Rachmanim, etc.

2. Because it is a positive Mitzvah to mimic G-d in His positive traits (Rambam Deos 1,6) - so if He is Rachum and skips, deters or postpones punishment (see Rambam Hilchos Teshuvah that G-d forgives and pardons and ignores our misdeeds) we are commanded to do so.

3. After all, we do have various mechanisms of preferring teaching Zchus over Chova - swaying the judgment toward exempting from punishment (only applies to the death punishment).

So imagine a woman suffering domestic violence and abuse from her husband who also refuses to divorce her. She has no authority to complain to and the court plays powerless in helping her out. One day she decides to kill him in a cold blood in front of 2 Kosher witnesses that warn her and she confirms the warning. She's taken to the court and the court, while finding her clearly guilty, pardons her from being executed.

So in the Jewish criminal law (corporal or death punishment) is there a concept of מוחלין מן הדין - unlawfully pardoning a sinner (out of true considerations of course) and if not - why is that?

Answer 1

The idea of letting off all death penalty defendants was broached in the Mishnah (Makkot 7a):

רבי טרפון ורבי עקיבא אומרים אילו היינו בסנהדרין לא נהרג אדם מעולם רשב״ג אומר אף הן מרבין שופכי דמים בישראל

R. TARFON AND R. AKIBA SAY: WERE WE MEMBERS OF A SANHEDRIN, NO PERSON WOULD EVER BE PUT TO DEATH. [THEREUPON] RABBAN SIMEON B. GAMALIEL REMARKED, [YEA] AND THEY WOULD ALSO MULTIPLY SHEDDERS OF BLOOD IN ISRAEL!

(Soncino translation, capitals in original)

The Talmud there explains how they would have achieved this:

היכי הוו עבדי רבי יוחנן ורבי אלעזר דאמרי תרוייהו ראיתם טריפה הרג שלם הרג אמר רב אשי אם תמצא לומר שלם הוה דלמא במקום סייף נקב הוה בבועל את הערוה היכי הוו עבדי אביי ורבא דאמרי תרוייהו ראיתם כמכחול בשפופרת ורבנן היכי דיינו כשמואל דאמר שמואל במנאפים משיראו כמנאפים

How could they [being judges] give effect to that [policy]? Both R. Johanan and R. Eleazar suggested that the witnesses might be plied with [intimate] questions such as, ‘Did you take note whether the victim was [perchance] suffering from some fatal affection or was he perfectly healthy?’ R. Ashi [enlarging on this] said: And should the reply be, ‘Perfectly healthy’, they might further be embarrassed by asking, ‘Maybe the sword only severed an internal lesion?’

And what would be asked, say, in a charge of incest? — Both Abaye and Raba suggested asking the witnesses whether they had seen the offenders as intimate as ‘kohl-flask and probe’?

Now [with regard to] the Rabbis, what kind of evidence [in such a charge] would they deem sufficient to convict? — According to Samuel's maxim; for Samuel said that being caught in the attitude of the unchaste is sufficient evidence.

(Soncino translation)

Answer 2

Note that it is often the opposite of merciful to exempt a person from punishment.

As Rabbi Simon ben Gamliel is quoted in Alex's answer as saying, not executing people who should be executed leads to more bloodshed. If murderers are let loose, innocent people would be murdered both because there would be more murderers around and because there would be no deterrent.

Thus letting a murderer off the hook is not kindness and valuing of life, but rather cruelty and sacrifice of innocent victims in order to protect criminals.

The same applies to rapists. Protecting them certainly harms existing and future victims.

(As a side note, I find the lack of punishment specified by the Torah for someone who raped a little girl or a woman who is not married and not a close relative of his extremely disheartening.)

The Halachic requirements to find someone guilty at a level which demands execution are so strict and almost impossible to be met, that a Sanhedrin which executed more than one person over the course of 70 years would have been considered murderous. As such, once a person has been found guilty at a level which necessitates execution, you can be assured that according to the Torah, he really absolutely deserved it. Hence there is no room for being even more lenient.

On the other hand, say there is someone going around raping young girls and nothing can be done to stop him. The Beit Din should be able to punish him severely in order to prevent more rapes. (Again, why a person who raped a little girl or any unmarried woman wouldn't be sentenced to death by the Torah while a person who lit a fire on Shabbat was is totally beyond me. As is much of the Torah's attitude towards rape of young girls.)