The Righteous Suffering for the Generation - a Jewish Concept

I recently posted about how Rav Mordechai Eliyahu (may he have a Refuah Sheleima) is suffering to bring Mashiah. An anonymous commenter took issue with this idea and said:

I am not aware that it is a Jewish concept that one Jew should suffer for another Jew's sins.We know that Teshuva and Ahavat Yisroel will bring the Moshiach,and that this is the work of every G-d fearing Jew.

While I agree with the second half of this statement, I will show that Talmidei Hachamim suffering for the sins of the generation is not something another religion made up - it was stolen from Jewish belief and then bastardized.

• Mesechet Nega'im 2:1:
  רבי ישמעאל אומר בני ישראל אני כפרתן (Ribbi Yishmael says: Benei Yisra'el - I am their attonement) and Ribbi Ovadia MiBartenura explains what Ribbi Yishmael means as: כל העונש שראוי לבא עליהן אני מקבל על עצמי כדי לכפר עליהן (any punishment that is worthy to come upon them, I accept upon myself in order to atone for them)
• Tanna DeVei Eliyahu Rabba 27:4:
  עליו הכתוב אומר (ישעיה נג)מעמל נפשו יראה ישבע וגו' . מכאן אמרו הת׳״ח שבדור הוא סובל עונות הדור שבתוכו בינו לבין עצמו ואין כל בריה יכולה להכיר בהן אלא הקביה לבדו ועליו הכתוב אומר (שם) ועונותם הוא יסבול
  ...Upon him, the verse says, (Yishaya 53:11) "Of the travail of his soul he shall see to the full..." From here, [Haza"l] said: A Torah scholar of the generation suffers the sins of that generation by himself and no creation is able to recognize this - only Hashem alone. Upon him, the verse says, "and their iniquities he did bear."
• Bava Metzia 84b-85a: Ribbi Elazar BeRibbi Shimon had terrible suffering. Kohelet Rabba 11:7 quotes his wife, who quotes him as saying "All the suffering of Israel should come upon me," and it did. (והוה אמר דכל יסוריהון דישראל ייתון עלי והיינון אתיין)
• Sanhedrin 39a: After a Min asked Ribbi Avahu why Yehezkel had to lay on his sides, he replied:מנהגו של עולם מלך בשר ודם שסרחה עליו מדינה אם אכזרי הוא הורג את כולן אם רחמן הוא הורג חצים אם רחמן מלא רחמים הוא מייסר הגדולים שבהן ביסורין אף כך הקב"ה מייסר את יחזקאל כדי למרק עונותיהם של ישראל The conduct of the world is that when a country rebels against a king of flesh and blood, if the king is cruel, he will kill them all. If he's merciful, he will kill out half. If he's full of mercy, he will cause the great men of them to suffer. Similarly, Hashem caused suffering to Yehezkel to wipe away the sins of Israel
• Ramban Shemot 32:32: ולפי דעתי כי משה אמר ועתה
  תשא חטאתם ברחמיך ואם אין מחני נא תחתם מספר החיים
  ואסבול אני ענשם כענין שאמר הכתוב והוא מחולל מפשעינו
  מדוכא מעונותינו מוסר שלומנו עליו ובחבורתו נרפא לנו And according to my opinion, Moshe said, "And now, bear their sin with Your mercy. And if not, please wipe me out in their place from the book of life, and I will suffer their punishment, as the verse says, "But he was wounded because of our transgressions, he was crushed because of our iniquities: the chastisement of our welfare was upon him, and with his stripes we were healed." (To which Hashem said, "No - for this sin, only those who sinned will be wiped out.")
• Derech Hashem 2:3:8:

  ואמנם ע״פ שורש זה, נסדר שיגיעו צרות ויסורין לאיש צדיק, ויהי׳ זה לכפרת דורו.
  והנה מחיוב הצדיקים, הוא לקבל באהבה היסורין שיזדמנו לו לתועלת דורו.
  כמו שהי׳ מקבל באהבה, היסורין שהיו ראוים לו מצד עצמו. ובמעשה הזה
  מטיב לדורו שמכפר עליו, והוא עצמו מתעלה עילוי גדול. שנעשה מן הראשים
  בקיבוץ בני העוה״ב וכמ״ש. ואולם מזה הסוג עצמו, ימצא עוד מין אחר
  יותר גבוה במעלתו מאותו שזכרנו, וזה כי מה שזכרנו הוא שילקה הצדיק
  על בני דורו, שהי׳ ראוים לעונש גדול מאד, וקרובים לכליה או לאבדון, והוא
  ביסוריו מכפר עליהם ומצילם בעוה״ז, ומועיל להם גם לעוה״ב. אמנם יש
  עוד יסורין, שנותנים לחסידים היותר גדולים המושלמים כבר בעצמם, והם
  לעזור למה שצריך לכלל גלגולי ההנהגה, שיגיעו אל הסוף שהוא השלימות.

  
  However, according to this concept, we can arrange [to say] that troubles and suffering will reach a righteous man, and this will be as an atonement for his generation. And one of the obligations of the righteous is to accept suffering that will occur to him with love for the benefit of his generation just as he accepts with love the suffering that were worthy for him for his own self. And with this act, he does good for his generation for he atones for it, and he himself ascends a great ascent - since he becomes one of the heads in the gathering of those who are worthy for the next world, as I stated. However, from this category itself, another type that is on an even higher level from what we mentioned can be found. And that is because what we mentioned is that the righteous man will be punished for the members of his generation, who were deserving of a very great punishment, and they were close to destruction or annihilation, but he with his suffering atones for them and saves them in this world, and it also helps them in the next world. However, there is yet further suffering that is given to the pious who are greater and have perfected themselves already. This [suffering] comes to help what is needed for the cycle of direction, which will reach the end, which is the perfected world...

  This last part seems to say that there are those that suffer to help bring Mashiah. The Derech Hashem goes on to explain this concept further. Look inside for his explanation.

Many more proofs exist for this concept, especially in Zohar.