How does the blood of a Rabbi atone for others? And where is it found in Rabbinic writings?
B"H, 29 Kislev 5771, 5th candle of Chanuka First allow me to clarify that there is no mention of the "blood" of the Rabbis which atones rather the death of "Tzaddikim"=the righteous which atones. It is mentioned in the Talmud Moed Katan 28a and Vayikra Rabba 20. In order to preclude the non-Jewish concept on this issue it should be clear that there is no Jewish teaching of a person giving up his life on his own in order to atone for others. The Jewish idea of closeness to G-D and piety is when a person embodies in his daily life the principles of the Torah and does not give up life. Only in extreme circumstances when a Jew is forcibly converted under various conditions is he required to face death rather than relinquish faith in G-D.(See Kuzari 3:20) Even to restrict oneself from permitted bodily needs and desires is considered sinful. (Talmud Nazir 10a). As to the question itself, the idea of the righteous atoning for others according to some commentaries is similar to any other punishment of a person which atones. (Menorat Hamaor 212). Rav Yonatan Eibshitz zt"l says that since the Talmud compares the death of the righteous to the atonement of the Para Aduma= red heifer, a similar principle applies. Just as the atonement of the Para Aduma is something without explanation, similarly the death of a Tzaddik though beyond our understanding it brings about atonement. According to some the death of a Tzaadik alone does not bring about atonement on its own without repentance. (Rav Yonatan Eibshitz Ye'arot Dvash Part I Drush 4) There is a lot more to be said and studied on this issue and I have only given you selected thoughts.