Gemara

45b (Bei Rav): If the spinal cord became Nismasmes, it is Tereifah; if it was Nismazmez (part of the interior flowed out), it is Kosher.

Objection: Levi saw a man bang his head, and Levi lamented, 'his brain was Nismazmez'! (He lamented that the man will die!)

Answer (Abaye): No, he lamented that the man cannot have children.

57b (Beraisa): If there is a long hole in the skull, or many small holes that add up to the area of a drill (it is Tereifah);

R. Yosi ben ha'Meshulam says, a case occurred in which a man's skull was pierced. They covered over it with a gourd, and he lived.

R. Shimon ben Elazar: This does not prove (that this is not a Tereifah). He was hurt in summer, and he died that winter!

Yevamos 114b (Rava): When there is war in the world, a woman is not believed to say that her husband died, lest he was hit by an arrow or spear, and she doesn't know that such wounds can be bandaged, and he can live.

120b (Beraisa): We can testify that a cut up person died;

R. Shimon ben Elazar disagrees, for he could be cauterized and live.

(Mishnah): A case occurred in which a man was lowered into water. When they lifted him, only his leg came up. Chachamim ruled that his wife may remarry only if more than the knee came up.

Suggestion: This is unlike R. Shimon ben Elazar!

Rejection: He could agree to this, for water aggravates the wound.

Nidah 23b (Rava): Tum'as Yoledes applies even if the baby was born with a punctured Veshet (foodpipe), but not if his Veshet is Atum (sealed).

(Beraisa - Rebbi): There is no Tum'as Yoledes for an Atum baby if it lacks at the bottom, to the point that a person cannot live if this is missing.

(R. Zakai): (Atum means that) part of the thigh (and all below) is missing.

(R. Yanai): The rectum (and below) is missing.

(R. Yochanan): The navel (and below) is missing.

R. Zakai argues with R. Yanai (and R. Yochanan) about whether a Tereifah can live. (R. Zakai holds that he cannot live.)

Menachos 37a: Flimo asked 'if one has two heads, on which does he wear Tefilin?' Rebbi said that Flimo must be punished.

(Beraisa): If a (firstborn) son was born with two heads, the father must pay 10 Shekalim to redeem him (five for each head).

Question: Rami bar Chama learned from "Ach" that some babies are not redeemed (e.g. a baby that was Nitraf)!

Answer: "Chameshes Shekalim la'Gulgoles" obligates redeeming every head.

Rishonim

Rambam (Hilchos Gerushin 13:16): if a man was cast into water, and they sent a trap after him, and came up a limb that he cannot live without it, we may testify that he died to permit his wife to remarry.

Magid Mishneh: The Ramban and Rashba say that they permitted the man only after 12 months. Also the Yerushalmi says so.

Kesef Mishneh: This is difficult, for in Chulin we say that a human Tereifah can live more than 12 months.

Hagahos Tosfos Yom Tov (on Tur EH 17:32): I did not find this. This is unlike Tosfos (Gitin 56b DH v'Niker, Zevachim 116a DH Dilma).

Rambam (18): If a man was stabbed or pierced by arrows, one may not testify about him that he died.

Toras ha'Bayis (Beis 2 Sha'ar 3 49b): R. Yosi cited a case in which someone with a hole in the skull was cured (to prove that this is not a Tereifah), and R. Shimon answered that he died that winter. This shows that even a cure will not enable a Tereifah to live (12 months).

Rashba (Nidah 23b DH Omar): Rashi explains that Rava (who says that there is Tum'as Yoledes for a baby born with a punctured Veshet) holds that a Tereifah can live, for we say that R. Yanai must hold that a Tereifah can live (for he holds that it does not suffice to be Atum from the thigh). Presumably, Rava holds like the Halachah that a Tereifah cannot live. Also, there is Tum'as Yoledes even for a Nefel! A Tereifah is no worse than a baby that was cut up before it left the womb (there is Tum'as Yoledes). The Ramban explains that Rava can hold that a Tereifah cannot live. A Tereifah baby could receive a Neshamah and live almost 12 months. Also, perhaps it was born healthy, and later the Veshet was punctured. We say below that they argue about whether or not a Tereifah can live. Tum'as Yoledes does not depend on this. Rather, the Beraisa gave a Siman, that if a baby is Atum so much that such that a person lacking this cannot live, there is no Tum'as Yoledes. The Amora'im argue about how much must a person be lacking so that he cannot live. We infer from their opinions that they argue about whether a Tereifah can live.

Chasam Sofer (YD 52): The Rashba explains that Rebbi had a tradition that such a Shi'ur of Atum is not considered a child. It is not because it is a Tereifah. The Rambam must agree. He is Machshir a baby born missing anything whose removal makes a Tereifah. A baby born missing the leg up to the thigh is Kosher. However, how can Amora'im hold that Rebbi holds that a Tereifah can live? He holds that a baby born with two heads cannot live! In Chulin 57b, he holds that a Tereifah cannot live more than 30 days. However, in the text of Tosfos (Zevachim 69b DH Iy), R. Meir said so. The Rambam rules that Tum'as Yoledes applies unless it is Atum until the navel, and he rules that a Tereifah cannot live! He rules that an animal has Tum'as Neveilah while alive if the thigh was removed and its cavity, but he does not say so about people, for the reason I gave. The Kesef Mishneh questions those who rule like the Yerushalmi, which requires her to wait 12 months, since loss of a thigh does not make man a Tereifah.

Tosfos (Menachos 37a DH Shome'a): The Beraisa exempts from Pidyon ha'Ben a baby that became Tereifah within 30 days.

Levush (YD 57:19): Any Tereifah from birth can live more than 12 months; in any case it is forbidden.

Shach (YD 57:48): The Rashba holds that any Tereifah due to something extra could live a long time, but it is considered Tereifah.

Kutnos Or (Bamidbar, brought in Mishneh Halachos 16:37): Why does Tosfos exempt Tereifos from Pidyon ha'Ben? "La'Gulgoles" should obligate any Tereifah with a head! Based on the Shach, we can say that we obligate only a Tereifah due to something extra, for it can live.

Poskim

Shulchan Aruch (EH 17:31): If a man was stabbed or pierced by arrows, one may not testify about him that he died.

Bach (DH u'Mah she'Chosav Oh): The Tur says that even if he was full of wounds in a place that makes him a Tereifah, we cannot testify about him, like R. Shimon ben Elazar, lest he was cauterized. We thought that the Mishnah is unlike R. Shimon, for he holds that even a leg cut at the thigh could be healed (if not that water aggravates the wound). It seems that the Rambam agrees that she may not remarry until 12 months.

Rebuttal (Chelkas Mechokek 59): The conclusion is that R. Shimon holds that she may never remarry, lest her husband was healed.

Beis Shmuel (94): The Chelkas Mechokek is correct. The Nimukei Yosef says that cauterizing does not help in a place that makes one a Tereifah.

Keren Orah (Yevamos 129b DH v'Chasvu): If a hot knife helps, R. Shimon should argue about all Tereifos! We must say like the Rashba, that R. Shimon is Machshir above the knee because this Tereifah was not a tradition. The Rambam connotes that he permits immediately, i.e. because water aggravates the wound. Since he holds that a Tereifah can be cured, perhaps one may not testify about a Tereifah after 12 months.

Shulchan Aruch (32): If a rope was tied around a man's leg and he was lowered into water, and only the leg came up [and part is] above the thigh, his wife may remarry after 12 months, for a Tereifah cannot live 12 months.

Beis Yosef (DH u'Mah she'Chosav): The Yerushalmi says that they permitted her only after 12 months.

Beis Shmuel (17:97): Perhaps since the Mishnah permits his wife to remarry, this shows that we hold that this Tereifah (the leg was cut above the knee) cannot live 12 months.

Beis Shmuel (first edition, 17:85): Since the Mishnah did not say when she may remarry, surely this is like other Tereifos, and he dies within 12 months.

Igros Moshe (CM 2:73:4): Nowadays everyone know that many Tereifos live long lives. Doctors cut the Sanya Divi (blind gut) in millions of youths, and they live to old age and do work like healthy people.