Gemara

(Rava): "Va'Chay Bahem" - one does not forfeit his life to avoid transgressing.

Contradiction: "V'Lo Sechalelu Es Shem Kodshi" - one may not transgress, even b'Ones!

Resolution: In private, "va'Chay Bahem." In public, "v'Lo Sechalelu..."

Kesuvos 19a (Rav Chisda): R. Meir says that witnesses are not believed to say that they were forced to sign. He holds that witnesses should forfeit their lives rather than sign falsely.

Objection (Rava): If they would ask us, we would tell them to sign and live. Why shouldn't we believe them?! One may transgress anything to save a life, except for idolatry, incest, or murder.

Bava Kama 60b (Rav Huna): Plishtim were hiding in stacks of barley of Yisrael. David asked whether he may use others' money (burn the stacks) to save himself. The Sanhedrin answered that a commoner may not, but a king may.

81a (Beraisa): Yehoshua stipulated that one lost in a vineyard may cut vines until he finds his way to the road.

Rishonim

Rosh (Bava Kama 6:12): David did not ask whether he may burn others' property to save Yisre'elim. Obviously, one may transgress anything for Piku'ach Nefesh other than the three Aveiros! Rather, he asked whether he may burn them without intent to pay for them. The answer was that one may not save without intent to pay.

Rashi (60b DH v'Yatzilah): The Sanhedrin ruled that he may not burn the stacks, for one may not save himself with another's money.

Shitah Mekubetzes (Kesuvos 19a DH Omar): The Ramban says that Rav Chisda explains that R. Meir holds that it is Midas Chasidus to be Moser Nefesh and not sign Sheker. If witnesses sign, they are called Resha'im. R. Meir does not believe a witness to make himself a Rasha even in this sense. Some say that Rav Chisda explains letter of the law. A Beraisa (not in Shas) says that R. Meir holds that theft is a fourth Aveirah that Piku'ach Nefesh does not override. Rava rejected this, for we rule like Chachamim. This is wrong. The Rashba rejects this, for ruling like Chachamim does not show what R. Meir holds. The Ro'oh says that also Rav Chisda normally forbids Midas Chasidus when one is exempt from Mesiras Nefesh; signing Sheker is an exception. The best Perush is that people despise false testimony so much that the custom is to be Moser Nefesh for this. Rava rejects this, for we would tell them not to. The Ritva says that only Gedolei ha'Dor like Chananyah, Misha'el and Azaryah may opt to be Moser Nefesh. Rather, people err and think that it is Midas Chasidus. It seems that Rashi holds like this.

Binyan Tziyon (168): The Ramban explains that even according to the Beraisa, R. Meir says that Piku'ach Nefesh does not override theft, but agrees that it overrides signing Sheker. Signing Sheker is not theft; the witnesses do not steal. The latter opinion holds that it is like Garmi, e.g. mistaken judgment. Since R. Meir obligates for Garmi (and the Halachah follows him), this is like theft. Rava holds that it is unlike theft.

Chasam Sofer (CM 1 Sof DH Re'eh): R. Meir did not bring a verse to show that Piku'ach Nefesh does not override theft. Presumably, it is because it is the nature of people to fight one who takes their money (this is why one may kill a thief tunneling into a house), and it might lead to murder.

Or Gadol (p. 21): Yehoshua stipulated that one lost in a vineyard may cut vines until he finds his way to the road. Rashi holds that only in this case one may save his life with another's money. We do not learn to other cases.

Poskim

Shulchan Aruch (CM 359:4): Even if one is in mortal danger and must steal to save himself, he may take only with intent to pay.

Maharatz Chayos (Bava Kama 60b DH Rashi): Parshas Derachim (19, 43a) says that Rashi (DH v'Yatzilu) learns simply that one may not save himself with another's money, even for Piku'ach Nefesh, and challenges this. The Yerushalmi (Avodah Zarah 2:2) obligates Mesiras Nefesh rather than to steal! Pnei Moshe suggests that perhaps the Yerushalmi holds like R. Meir, who says that witnesses should forfeit their lives and not sign Sheker.

Binyan Tziyon (1:167): Tosfos and the Rosh are difficult. The Gemara says that the question was whether one may save himself with another's money, not whether or not he is liable! Rashi explains that one may not steal for Piku'ach Nefesh. Most Rishonim did not explicitly discuss this. The Rambam obligates one who stole (to save himself), but does not say whether it is permitted l'Chatchilah.

Hafla'ah (Kesuvos 19a Tosfos DH v'Omar): Rav Chisda did not err to think that R. Meir obligates Mesiras Nefesh to avoid false testimony. Rather, Rav Chisda discussed only an Anas who intended to kill the witnesses. (In CM 292 and 388, we distinguish whether or not the Anas intended to take from the person he confronted.) Then, they may not exempt themselves by signing Sheker against another. He forbids stealing from or causing a loss to another to heal oneself. Rava responded that even in this case, one may transgress anything except for the three Aveiros. If an Anas wanted Levi's money, and if he does not get it he will take Levi's, and Levi showed him David's, the Ramban, Rashba and others exempt Levi. If so, witnesses who signed Sheker in such a case would be Kesherim! Also, we should divide their words and only 'hear' that they were forced for money, but not that the Anas wanted their money (rather, we assume that he wanted the money of the one they signed about, and they are Kesherim)! We must say that one who was coerced may show others' money, but he may not do an act. Signing is an act (so in any case they transgressed).

Binyan Tziyon (167): R. Akiva (Yoma 85) says that Shabbos overrides a limb, all the more so Piku'ach Nefesh overrides Shabbos because Avodah overrides Shabbos and Piku'ach Nefesh overrides Avodah. Surely, even though we are Mechalel Shabbos to offer Temidim and Musafim on Shabbos, one may not steal an animal even if there is no other way to get an animal for the Korban! A verse disqualifies a stolen animal for a Korban. It does not distinguish whether or not one can find another animal. Just like Avodah does not override theft, also Piku'ach Nefesh does not override theft.

Question: Avodah does not override theft because Hash-m does not desire such a Korban! If there is no male for the Tamid, we would not bring a female! The Gemara asked how we know that Piku'ach Nefesh overrides Shabbos. It did not ask about overriding theft. This is because we kill people for Chilul Shabbos, therefore one might have thought that Piku'ach Nefesh does not override it. What is needed for Avodah is not called Chilul. All the more so, Chilul Shabbos for Piku'ach Nefesh is not called Chilul.

Answer (Binyan Tziyon 168): The Ramban and Rashba said that Rav Chisda discusses mere Midas Chasidus; they questioned Rashi, who says that it is letter of the law. Rashi explains that Rav Huna, who said that David asked about saving himself with another's money, holds like Rav Chisda. Rava, who argues with Rav Chisda, explained David's question differently.