If someone caused pain to multiple people or caused irreversible damage, can he possibly be in a situation where he can no longer do teshuvah? If so, what does hashem want from him at this juncture?
There is no sin of such a great magnitude that it is beyond teshuva. (Rambam's Hilkhot Teshuva 1:3).
Indeed, the Talmud Gittin (57b) recounts that even the murderous Nevuzaradan did teshuva.
However, Rambam writes (Hilkhot Teshuva 2:9) that interpersonal sins require restitution to the victims, and one is not forgiven until they forgive him. Nevertheless, if one does his best to appease the victims, but to no avail, that seems to be enough (ibid). Furthermore, he further writes (4:3) that the difficulty in such cases is to do "full teshuva". Apparently, even in cases of harm to others, partial teshuva is possible.
In a case where one harmed the public and doesn't know whom to recompense, as for example, with someone who stole public funds, he should perform public services as a general way of giving back to the public he harmed (Shulhan Arukh Hoshen Mishpat 366:2).
There are a few sins which, at first glance, are impossible to repent over:
The Mishna in Chagiga says:
רַבִּי שִׁמְעוֹן בֶּן מְנַסְיָא אוֹמֵר, אֵיזֶהוּ מְעֻוָּת שֶׁאֵינוֹ יָכוֹל לִתְקֹן, זֶה הַבָּא עַל הָעֶרְוָה וְהוֹלִיד מִמֶּנָּה מַמְזֵר. אִם תֹּאמַר בְּגוֹנֵב וְגוֹזֵל, יָכוֹל הוּא לְהַחֲזִירוֹ וִיתַקֵּן. רַבִּי שִׁמְעוֹן בֶּן יוֹחַאי אוֹמֵר, אֵין קוֹרִין מְעֻוָּת אֶלָּא לְמִי שֶׁהָיָה מְתֻקָּן בַּתְּחִלָּה וְנִתְעַוֵּת, וְאֵיזֶה, זֶה תַּלְמִיד חָכָם הַפּוֹרֵשׁ מִן הַתּוֹרָה:
Rabbi Shimon ben Menassia says: What is "a crooked thing that cannot be fixed"? This applies to one who had relations with a forbidden woman and fathers a mamzer through her. If you would say [the verse refers to] a thief or a robber, he can return it and make amends. Rabbi Shimon ben Yochai says: One is only called "crooked" if he was proper at first and became crooked; and who is that? A Sage who separates from Torah.
The Gemara and Rashi says that the reason is that this sin has permanent effects, one cannot atone for it.
A Mishna in Yoma says:
הָאוֹמֵר, אֶחֱטָא וְאָשׁוּב, אֶחֱטָא וְאָשׁוּב, אֵין מַסְפִּיקִין בְּיָדוֹ לַעֲשׂוֹת תְּשׁוּבָה. אֶחֱטָא וְיוֹם הַכִּפּוּרִים מְכַפֵּר, אֵין יוֹם הַכִּפּוּרִים מְכַפֵּר. עֲבֵרוֹת שֶׁבֵּין אָדָם לַמָּקוֹם, יוֹם הַכִּפּוּרִים מְכַפֵּר. עֲבֵרוֹת שֶׁבֵּין אָדָם לַחֲבֵרוֹ, אֵין יוֹם הַכִּפּוּרִים מְכַפֵּר, עַד שֶׁיְּרַצֶּה אֶת חֲבֵרוֹ. אֶת זוֹ דָּרַשׁ רַבִּי אֶלְעָזָר בֶּן עֲזַרְיָה, מִכֹּל חַטֹּאתֵיכֶם לִפְנֵי יְיָ תִּטְהָרוּ (ויקרא טז), עֲבֵרוֹת שֶׁבֵּין אָדָם לַמָּקוֹם, יוֹם הַכִּפּוּרִים מְכַפֵּר. עֲבֵרוֹת שֶׁבֵּין אָדָם לַחֲבֵרוֹ, אֵין יוֹם הַכִּפּוּרִים מְכַפֵּר, עַד שֶׁיְּרַצֶּה אֶת חֲבֵרוֹ. אָמַר רַבִּי עֲקִיבָא, אַשְׁרֵיכֶם יִשְׂרָאֵל, לִפְנֵי מִי אַתֶּם מִטַּהֲרִין, וּמִי מְטַהֵר אֶתְכֶם, אֲבִיכֶם שֶׁבַּשָּׁמַיִם, שֶׁנֶּאֱמַר (יחזקאל לו), וְזָרַקְתִּי עֲלֵיכֶם מַיִם טְהוֹרִים וּטְהַרְתֶּם. וְאוֹמֵר (ירמיה יז), מִקְוֵה יִשְׂרָאֵל יְיָ, מַה מִּקְוֶה מְטַהֵר אֶת הַטְּמֵאִים, אַף הַקָּדוֹשׁ בָּרוּךְ הוּא מְטַהֵר אֶת יִשְׂרָאֵל:
One who says, "I will sin, and then repent, I will sin [again], and then repent," will not receive an opportunity to repent; [for one who says] "I will sin, and Yom Kipur will atone," Yom Kippur will not atone. Yom Kippur atones for transgressions between a person and God, but for a transgression against one's neighbor, Yom Kipur cannot atone, until he appeases his neighbor. Thus R. Eleazar ben Azariah expounds the text, "From all your sins before the Lord shall ye be clean": For transgressions between a person and God, Yom Kippur atones, for transgressions against one's neighbor, Yom Kippur cannot atone, until he appeases his neighbor. R. Akiva says, Happy are you, Israel! Before whom are you purified, and who purifies you [of your transgressions]? Your Father Who is in heaven. For it is said, "Then will I sprinkle clean water upon you, and ye shall be clean"; and it is also said, "The ritual bath [lit. Hope] of Israel is the Lord"; even as a ritual bath purifies the unclean, so does the Holy One, Blessed be He, purify Israel.
A Mishna in Avos says:
וְכָל הַמַּחֲטִיא אֶת הָרַבִּים, אֵין מַסְפִּיקִין בְּיָדוֹ לַעֲשׂוֹת תְּשׁוּבָה
Anyone who brings merit to the many, sin does not result from him. And anyone who brings the many to sin is not given enough [time] to repent.
The Gemara says that the reason is:
וכל המחטיא את הרבים אין מספיקין בידו לעשות תשובה שלא יהא הוא בגן עדן ותלמידיו בגיהנם שנאמר (משלי כח, יז) אדם עשוק בדם נפש עד בור ינוס אל יתמכו בו
On the other hand, whoever causes the public to sin has almost no ability to repent, so that he will not be in the Garden of Eden while his students are in Gehenna, as it is stated: “A man who is laden with the blood of any person shall hasten his steps to the pit; none will support him” (Proverbs 28:17). Since he oppressed others and caused them to sin, he shall have no escape.
However, there are a few counter-points:
While one can't undo his actions and undo the Mamzer's creation, if one repents he is still considered a good Jew, as the Gemara says in Yevamos:
והאי בר תשובה הוא והתנן שמעון בן מנסיא אומר איזהו (קהלת א, טו) מעוות לא יוכל לתקון זה הבא על הערוה והוליד ממנה ממזר השתא מיהא עושה מעשה עמך הוא:
The Gemara objects: Is he in fact able to repent after fathering a mamzer? Didn’t we learn in a mishna that Shimon ben Menasya says: Which is: “That which is crooked cannot be made straight” (Ecclesiastes 1:15)? This is referring to one who engaged in intercourse with a relative who is forbidden to him and fathered a mamzer with her. This implies that he has no possibility of achieving total repentance. The Gemara responds: At least now, after repenting, he is considered as one who acts according to the deeds of your people. Although he cannot totally rectify his transgression, his child is liable to receive punishment for cursing or hitting him.
- The Ikkar Tosfos Yom Tov writes:
כמו אמרם אין מספיקין בידו לעשות תשובה. ולפיכך לא יעזרהו השם שיעשה בצום כפור מה שראוי לו לעשות כדי שיכפרו לו עונותיו באותו היום. Hashem won't help him have a proper Yom Kippur so he won't achieve atonement.
Though one can imply (As Rabbi Shneur Zalman of Liadi did) that
ואף גם זאת "אין מספיקין" דייקא; אבל אם דחק ונתחזק ונתגבר על יצרו ועשה תשובה, מקבלין תשובתו. Withal he is not granted an opportunity. But if he pressed forcefully and overpowered his evil impulse and did repent, then his repentance is accepted.
I'm just offering a completely different approach to this question.
From our sources it is clear that there are two different ways of Teshuva - one being strictly Halakhic and established and the other being kind of miraculous, Hashem aided.
THe first is well defined by Rambam's Hilkhos Teshuva and everyone that follows them knows exactly what's expected and when he's completely forgiven (if anything).
The later leaves Hashem an option to override those rules and offers a shortcut to a full Teshuvah (thru Hashem's forgiveness) in cases where the established Halakha sees no way of repent. Those are the cases with R' Elazar ben Dordaysh, Menashe and others.
That teaches us "עת לעשות לה' - this is the Halakha, but "הפירו תורתך" it is always possible to override it (Tehhilim 119).