Gemara

(R. Avahu): We throw into a pit Mumarim (people who sin to anger Hash-m), Mosrim... We do not raise them.

Bava Kama 117a: Yosef wanted to show Yehudah's straw (to extortionists). Rav told him not to. He persisted 'I will show.' Rav Kahana broke Yosef's neckbone.

Rav: "...Like a trapped wild ox" - once a wild ox is trapped, no one has mercy on it. Similarly, once money of Yisrael falls into the hands of Nochrim, they have no mercy on it.

119a (Rav Huna or Rav Yehudah): One may destroy property of a Moser.

Since one may kill him, all the more he may destroy his money!

Berachos 58a: Rav Shila lashed a man (Ploni) who had relations with a Mitzris. The man informed on him to the king, that a Yisrael who judges without permission of the king. The king sent to take Rav Shila.

Rav Shila said that Ploni had had relations with a donkey. Eliyahu came, looking like a commoner, and testified to this. The court gave to Rav Shila a staff and authority to judge. He explained to Ploni that Mitzriyim are equated to donkeys -- "Asher Besar Chamorim Besaram."

Rav Shila saw that Ploni was going to report this to the king. Rav Shila reasoned 'the Torah says that if one seeks to kill you, kill him first!' He killed him.

Rishonim

Rambam (Hilchos Chovel u'Mazik 8:10): Once one says 'I will be Moser Ploni or his money', even a small sum, he permits himself to be killed. We warn him not to be Moser. If he is brazen and insists that he will, it is a Mitzvah to kill him. Whoever does so first, he merited.

Magid Mishneh: The Rambam learns from the episodes in Bava Kama and Berachos. In the latter episode, Ploni tried to kill Rav Shila. Even so, warning is required. Perhaps Rav Shila warned him. Alternatively, he didn't have time.

Mishneh l'Melech: The Rivash (473) says that Rav Shila warned him, or he didn't have time. The intended victim need not warn him! Only others must, like the case with Rav Kahana.

Hagahos Mishneh l'Melech: The Rivash himself (238) says that perhaps the victim need not warn him. He is frantic to save himself, so Chachamim did not obligate him to warn the Moser. Likewise, others may not kill a Rodef if it suffices to destroy a limb, but the Nirdaf need not be particular about this.

Kesef Mishneh (Hilchos Melachim 9:4): The Rambam permits a Nirdaf to kill a Rodef even if it suffices to destroy a limb. The Ra'avad challenges this from Avner; Yo'av justified killing him, for Avner could have stopped Asa'el without killing him (Sanhedrin 49a). The Rambam holds that this was false. The verse calls Avner a Tzadik! Rather, they had greater charges against Yo'av.

Mishneh l'Melech (Melachim 9:4): The Rambam means that Beis Din does not kill a Nirdaf who killed when he could have destroy a limb, but the Go'el ha'Dam of the Rodef (i.e. Yo'av) may kill the Nirdaf for doing so.

Rambam (Hilchos Rotze'ach 4:10): It is a Mitzvah to kill Yisrael idolaters, Mumarim... If one can kill them in public with a sword, he does so. If not, he seeks pretexts to cause their death. E.g. if one of them fell in a pit, he takes the ladder and says 'I will take my son down from the roof, then I will return it to you.'

Kesef Mishneh: Perhaps the Rambam's text of the Beraisa said 'Apikorsim' in place of 'Mosrim.'

Yam Shel Shlomo (ibid.): It seems that the Rif does not permit overtly killing a Moser. This is why he omitted the episode with Rav Kahana. Rav expounded to teach that Rav Kahana is not called a murderer, but Rav Kahana erred, and therefore he accepted to do Teshuvah. Also R. Tam does not permit overtly killing a Moser. One opinion (Bava Kama 119a) holds that since one may cause his death, all the more so one may overtly destroy his property.

Rebuttal (Shach CM 388:56): This is not a Kal va'Chomer! The Gemara connotes otherwise. Surely, the Rif does not hold that Rav Kahana did improperly! The Rif said that we are no more stringent about his money than about his life, so he did not need to bring the episode with Rav Kahana.

Yam Shel Shlomo (ibid.): The Rambam's text of the Beraisa did not include Moser. Further, the Rambam explains that the Beraisa permits lowering into a pit, and all the more so to overtly kill if one can. However, I hold that it does not permit killing overtly. Even so, one may overtly kill one who will be Moser. The Beraisa allows only lowering (but not overtly killing) after he was Moser, if there is no concern lest he do so again, e.g. he became despised in the eyes of the government. Rav Kahana was allowed to kill the Moser. He accepted to do Teshuvah for acting in front of his Rebbi without asking. Also, he endangered himself. The Yevanim did not tolerate murder; he should not have relied on a miracle.

The Tur (Sof 388) cites Ba'al ha'Itur who forbids overtly destroying his money, but permits through Gerama or even Garmi. I agree, but not through Mesirah to Nochrim, which is like overtly destroying. The Maharam and Mordechai (195) say so. Also, we do not destroy a Yisrael's money in a way that benefits transgressors. The Mordechai (194) permits keeping the Moser's money, for "the Rasha prepares, and the Tzadik will wear." This was a reason not to destroy it, lest the Moser have a righteous child. His child comes first! Rather, the lenient opinion permits even destroying his money, and all the more so to keep it. The stringent opinion forbids both.

Rambam (Hilchos Mamrim 3:2): If it is publicly known that one denies Oral Torah, he is like Mumarim, Mosrim... who are not part of Klal Yisrael. We throw them into a pit. We do not raise them. We do not need witnesses, warning or judges. Whoever afflicts them did a great Mitzvah and removed a stumbling block.

Beis Yosef (CM 388 DH uvi'Teshuvos): We must say that he discusses people established to be Moser.

Teshuvas ha'Rosh (32:4): The opinion that holds 'since one may kill a Moser, all the more he may destroy his money' refers to one who intends to be Moser. He is a Rodef; he may be killed in any way. One who was Moser may not be killed. Even a murderer is killed only in Beis Din, through witnesses and warning. We may cast him into a pit to die. One may cast an idolater to die, even though one may not kill someone going to do idolatry. Casting into a pit is only Gerama.

Question (Mishneh l'Melech Hilchos Malveh 5:2 DH u'Mah she'Chosav): Why did the Tur (CM 425) permit killing idolaters and Mumarim in any way, like the Rambam, without mentioning that the Rosh disagrees?

Rivash (238): The Rambam permits overtly killing a Rodef. R. Chananel permits only to cast him into a pit so he will die there, but not overtly killing him. Even R. Chananel would permit giving him to officers of the kingdom to kill him, for this is not overt. Also Teshuvas ha'Rosh says so.

Poskim

Shulchan Aruch (CM 388:10): Once one says 'I will be Moser Ploni or his money', he permits himself to be killed. We warn him not to be Moser. If he is brazen and insists that he will, it is a Mitzvah to kill him. Whoever does so first, he merited.

Rema: If there is no time to warn him, he need not be warned. Some say that one may not kill a Moser unless one cannot be saved from him by destroying one of his limbs, but if it suffices to cut out his tongue or blind him, one may not kill him, for he is no worse than other Rodfim.

Beis Yosef (DH uvi'Teshuvos): Teshuvos Maimoniyos (Nezikim 15) says so. This is difficult, for surely Rav Kahana could have cut the man's tongue or legs! The same applies to the case with Rav Shila.