Gemara

(Ze'iri): If the neckbone and most of the flesh were cut, the animal is a Neveilah.

32a (Mishnah #1 - R. Yeshevav): If one slaughtered the Veshet and uprooted the Kaneh, it is a Neveilah;

R. Akiva says, it is a Treifah.

(R. Yeshevav, citing R. Yehoshua): Any case in which the Shechitah was Pasul, the animal is a Neveilah. If it was slaughtered properly but something else forbids the animal, it is a Treifah.

R. Akiva retracted and agreed to R. Yeshevav.

Contradiction: Mishnah #2 shows that R. Akiva still disagrees!

(Mishnah #2): The following are Treifos: the Kaneh was uprooted...

Answer #1 (Reish Lakish): In Mishnah #1, he cut the Kaneh where its majority was already cut. This is a Pesul in the Shechitah itself (only one Siman was slaughtered). In Mishnah #2, he cut it elsewhere. The Shechitah was proper, just the animal itself was a Treifah.

Question: Reish Lakish himself taught (below) that if he slaughtered the Kaneh and then punctured the lungs, it is Kosher. This shows that once a Siman is cut, it (or any organ dependent on it) is as if it is in a basket (it no longer affects the animal's status). Here also, if the Kaneh was already cut, cutting it in a different place should not be considered Shechitah. The animal should be a Neveilah!

Answer #2 (R. Yochanan): R. Akiva taught Mishnah #2 before he retracted. Since Chachamim were used to the text of that Mishnah, it was not changed after he retracted.

(Reish Lakish): If he slaughtered the Kaneh and then punctured the lungs, it is Kosher.

(Rava): This applies only to the lungs, since their whole function depends on the Kaneh. If the innards were punctured (after cutting the Kaneh), it is forbidden.

Objection (R. Zeira): If you permit even though a wound that makes it a Treifah occurred after cutting one Siman, it makes no difference whether the wound was in the lungs or innards!

The following question shows that R. Zeira retracted.

Question (R. Zeira): If the innards were punctured after cutting one Siman, what is the law? Does the cutting of the first Siman join to the cutting of the second?

It is clear to R. Zeira that the animal is forbidden. He asks whether we consider the animal to be slaughtered (and only Treifah), or a Neveilah.

(Rav Acha bar Yakov): We may derive from Reish Lakish that a Yisrael may eat innards, but a Nochri may not;

For a Yisrael, Shechitah is needed to permit the animal. Shechitah permits the innards.

Shechitah is not needed for a Nochri. It depends only on whether the animal is dead. Therefore, for him, the innards are forbidden, like Ever Min ha'Chai (a limb from a living animal).

Rishonim

Rosh (2:11): One may cut a piece from an animal after proper Shechitah while it was quivering, and eat from it or feed it to a Nochri after the animal dies. This is unlike Rav Acha, for he holds like Reish Lakish. They hold that after Shechitah, it is as if the innards are in a basket, and death of the animal does not permit them. The same applies to meat cut after Shechitah, before it died. The Halachah does not follow them, rather, like R. Zeira's question. He holds that even after a Siman was cut, what was connected to it can forbid the animal. He did not retract from his question. He challenged Rava according to Rava's reasoning (that after a Siman was cut, what was connected to it cannot forbid the animal), but R. Zeira himself disagrees. Reish Lakish taught two laws that contradict each other. We do not know which he taught last, so we are stringent.

Ramban (Milchamos Hash-m 8a): What forced R. Chiya bar Aba to say that Mishnah #2 is unlike the Halachah? He could say that it discusses one who cut the Kaneh in a place where it was not yet cut! Rather, all agree that once the majority of the Kaneh was cut, making another cut is meaningless. They argue only about the lungs. Even though its life is due to the Kaneh, its life is also due to the Veshet, since the Kaneh and Veshet nurture from each other.

Poskim

Shulchan Aruch (YD 27:1): If one cut a piece from an animal after proper Shechitah while it was quivering, one may not eat from it until the animal dies.

Shach (2): The Heter to eat after it dies is only if it was slaughtered properly. If not, surely it is Ever Min ha'Chai for Yisrael and for Nochrim. The Rashba says so.

Question (Beis Yosef DH u'Mah): Why did the Tur need to write that a Pesul in Shechitah makes a Neveilah, and not a Tereifah? Both are forbidden. The only difference is Tum'ah. The Tur does not teach laws of Tum'ah (which do not apply nowadays), only Isur v'Heter!

Answer (Toras Chayim 20b DH Amar): The Rosh and Tur brought Zeiri's law, that if the neckbone and most of the flesh were cut, the animal is a Neveilah. Also, the Tur brought this right after 'if one cut a piece from an animal after proper Shechitah while it was quivering, one may feed the innards to a Nochri.' How are these connected? I answer that one might have thought that after cutting the Kaneh and Veshet, it is as if the lungs and innards were removed from the animal before it died, and are in a basket, so they are Ever Min ha'Chai for a Nochri. The Tur teaches that this is not so. Since it is permitted for Yisrael, it is permitted for Nochrim. Then he teaches that Pesulim in Shechitah make it a Neveilah, so in such cases one may not feed the innards to Nochrim. Since it is not considered Shechitah for Yisrael, it does not help for Nochrim, either. If something else disqualified the Shechitah, the Shechitah helped for Yisrael to be Metaher from Tum'as Neveilah, so it helps for Nochrim to permit Ever Min ha'Chai. If the neckbone and most of the flesh were cut, the animal is a Neveilah in its lifetime. Even if he slaughtered it, the innards are forbidden to Nochrim, for we cannot apply 'since it is permitted for Yisrael...'

Pri Chodosh (1): Maharshal says that even if a Yisrael slaughtered a Nochri's animal, it is as if a Nochri slaughtered it. This is unreasonable. Anything permitted to Yisrael is permitted to Nochrim! The Rashba distinguishes between Tahor and Tamei animals. This is because he rules like Reish Lakish, that if one slaughtered the Kaneh and afterwards the lung was punctured, it is Kosher, for it is as if they are in a basket. We hold (YD 26:2) that it is Tereifah, unlike Reish Lakish, i.e. that it is (this should say 'not') as if they are in a basket. If so, in every case it is permitted to a Nochri, unless it (or other meat) totally separated from the animal before it died. The same applies if one cut from a Tamei animal while it was quivering. Even if in the animal was later slaughtered properly, since Shechitah does not apply to it, the meat is forbidden to Nochrim. Toras Chayim says that if a Pesul occurred in the Shechitah and it does not Metaher from Tum'as Neveilah, the innards are forbidden to Nochrim. This is wrong. Since we rule unlike Reish Lakish, the innards are not Ever Min ha'Chai.

Rebuttal (Tevu'os Shor 5): He overlooked why the Poskim rule unlike Reish Lakish. The Ramban explains that Reish Lakish holds that the life of the lungs and innards depends on the Kaneh and Veshet, for (we hold that) they nurture from each other. Therefore, if only one Siman was cut, the Kaneh and Veshet are still 'alive'. However, after both Simanim were cut, all agree that it is as if they are in a basket. The Torah Chayim and Rashba say so. Rav Acha derived from Reish Lakish that a Nochri may not eat innards. Really, all agree to this, for both Simanim are cut! He mentioned Reish Lakish because he said 'it is as if they are in a basket', or because Rav Acha himself rules like Reish Lakish. The Ra'avad and Rosh rule like R. Zeira. Perhaps this is even if both Simanim were cut. I.e. the lungs and innards nurture from the rest of the body. If so, the death of the body affects them (and permits them to Nochrim). Reish Lakish was greater than R. Elazar, who preceded R. Zeira. Normally they would rule like Reish Lakish against him. Here they are stringent to rule like R. Zeira due to the contradiction in Reish Lakish's teachings.

Note: Some Rishonim say that we rule like the latter Amora from Abaye and Rava and onwards, and some say only after Abaye and Rava. R. Zeira was their contemporary. Tevu'os Shor assumes that the Ra'avad and Rosh hold like the latter opinion.

Tevu'os Shor: The Rashba says that the Rif omitted Reish Lakish's teaching, because he is stringent like R. Zeira. Even if you will say that R. Zeira explains Reish Lakish unlike Rava, and says that it is not as if they are in a basket, rather, Treifos does not apply when the animals is already half-dead (half-slaughtered), the Stam Gemara and Rav Acha hold like Rava. If so, we should rule like Reish Lakish according to Rava when this is a stringency. E.g. if one slaughtered one Siman and the animal died before he cut the second, a Nochri may not eat what was attached to the Siman.

R. Akiva Eiger (27:1): If the Veshet of a fattened goose was punctured until the interior, may one sell to a Nochri the innards and everything connected through the Kaneh and Veshet? The Shach brings from the Rashba that if it was not slaughtered properly, one may not cut off a limb while it is quivering and give it to a Nochri. If so, the innards are forbidden, for (after the Simanim are cut) it is as if they are in a basket. Toras Chayim says that this is why the Tur explained that a Pesul in Shechitah makes a Neveilah. The Ramban connotes that if both Simanim were cut, all agree that it is as if they are in a basket. If so, if it became Neveilah during the Shechitah, one may not sell the innards to a Nochri. The Torah Chayim, Tevu'os Shor and Kreisi u'Pleisi concluded like this. If so, since the Shulchan Aruch and Rambam rule that Shechitah does not helps if the Veshet was punctured, one may not sell the innards to a Nochri. However, why shouldn't Shechitah help? It seems that this is only when he cut the Veshet where (or opposite to where) it was punctured, for then the puncture joins with the cut, and part of the majority was not cut through Shechitah. However, if he cut above or below, it is only Tereifah, and one may not sell the innards to a Nochri.

Pischei Teshuvah (1): Bris Avraham (YD 23) was asked why about force-fed geese in which the Veshet was punctured, which is Neveilah. Why do we sell them, with the innards, to Nochrim? He gave proper reasons. One is that we forbid an animal that became Neveilah during the Shechitah, but we permit a bird. The Chasam Sofer (19) permits even regarding innards of animals.