Yuma 85a. The question was asked of the Tannaim: From where do we learn that saving a life supercedes Shabbos? Rabbi Shimon ben Menasia said, “And the children of Israel shall keep the Shabbos.” The Torah says: Violate one Shabbos for him, so that he may keep many Shabbosos. Rav Yehuda said in the name of Shmuel: Had I been there, I would have given an answer better than all of them: “Live by them” – and not die by them. Rava said: All of the arguments can be refuted except that of Shmuel, because the Tannaim’s arguments only work when one is certainly saving a life, but Shmuel’s works even when one is possibly saving a life.
יומא פה. נשאלה שאלה זו בפניהם: מניין לפקוח נפש שדוחה את השבת? …. רבי שמעון בן מנסיא אומר: (שמות לא) ושמרו בני ישראל את השבת, אמרה תורה: חלל עליו שבת אחת, כדי שישמור שבתות הרבה. אמר רב יהודה אמר שמואל: אי הואי התם הוה אמינא: דידי עדיפא מדידהו, (ויקרא יח) וחי בהם ־ ולא שימות בהם. אמר רבא: לכולהו אית להו פירכא, בר מדשמואל דלית ליה פרכא… אשכחן ודאי, ספק מנלן.
A man came to Rabbi Naftali Jaeger, Rosh Yeshiva of Sh’or Yoshuv, and asked the following question: The Rema (Orach Chaim 306:14) says that someone whose daughter was kidnapped by the priests for forced conversion must violate Shabbos to save her. In other words, saving someone from shmad has the same status as saving a life. If so, it should be allowed to violate Shabbos in order to do kiruv, for example driving to give shiurim or participate in a kiruv event. He said he had asked the question to many rabbis and no one had been able to answer.
Rabbi Jaeger did not have an answer either. But some time later, Rabbi Moshe Shapiro came to New York, and Rabbi Jaeger brought him to visit this man. The man presented his question, and Rabbi Shapiro answered immediately.
The Gemara in Yuma says that there are two reasons to violate Shabbos when saving a life: 1) “Violate one Shabbos so that he may keep many.” 2) Vachai bahem – “Live by them.” Rava then states that the principle of “violate one Shabbos” works only if the life will certainly be saved, but “vachai bahem” works even in a case where there is only a possibility of saving a life.
The Netziv (Haamek Sheilah 167:13) shows that there are cases when only “violate one Shabbos” works but not “vachai bahem.” In Bava Metzia 114b, the story is told that Rabbah bar Avuha met Eliyahu Hanavi in a non-Jewish cemetery. He asked, “Isn’t the Master a kohein?” Eliyahu replied that the graves of non-Jews do not contaminate their airspace. Tosafos asks: If Eliyahu was a kohein, how could he have touched the boy he brought back to life? Tosafos answers that he was certain that he would succeed in resurrecting him, so it was permitted for pikuach nefesh. The question is: if resurrecting a dead person is considered like saving a life, why did Tosafos have to say Eliyahu was sure he would succeed? Even if there was only a small chance of success, it should be allowed, just like pikuach nefesh pushes aside Shabbos even when there is a chance of success. The Netziv answers: “Vachai bahem” doesn’t apply when the person is already dead. But “violate one Shabbos” does – because indeed, after he comes back to life, he will be keeping many Shabbosos. And as Rava said in Yuma, “violate one Shabbos” works only in a case of certainty.
“Now we can answer your question very simply,” concluded R’ Moshe Shapiro. “Saving the girl from the priests may or may not be successful. But since she is still a religious Jew now, she is considered spiritually alive. The rule of ‘vachai bahem’ thus applies and one may violate Shabbos to save her. The secular Jews who are the targets of kiruv, on the other hand, are already spiritually dead. We are trying to bring them back to life. For bringing back to life, we don’t use ‘vachai bahem.’ The only reason to do it would be ‘violate one Shabbos so that he may keep many.’ And since we have only a chance of success, this principle doesn’t apply!”
Source: Shiur by Rabbi Naftali Jaeger, 7 Teves 5778