Gemara

(Rav Acha): Rami bar Yechezkel taught that Ikur (if the Simanim were uprooted, the Shechitah is Pasul) does not apply to birds. This is like the opinion that the Torah does not require Shechitah of birds;

The one who requires Shechitah of birds mid'Oraisa, holds that Ikur applies to birds.

Objection (Rav Ashi): Just the opposite! If Shechitah is mid'Oraisa, we can say that a tradition from Sinai teaches that Ikur does not apply to birds;

However, if Chachamim obligated Shechitah, presumably they would equate birds to animals for all laws of Shechitah!

28a (Beraisa): If the Veshet was slaughtered, and afterwards the Kaneh was uprooted, the Shechitah is Kosher. If the Kaneh was uprooted before Shechitah of the Veshet, it is invalid.

A case occurred in which it was not known if the Veshet was uprooted before or after the Shechitah. Chachamim forbade, like all cases of Safek Shechitah.

The Beraisa taught only about the Kaneh becoming uprooted, for it is rare for the Veshet to become uprooted.

42b (Rabah bar bar Chanah): If the Kaneh or Veshet (was uprooted, and) is mostly dangling, it is Tereifah.

44a (Shmuel): If the entire Turbatz Veshet (the place where the Veshet is attached to the jaw) was removed from the jaw, the animal is Kosher.

Support (Mishnah): If the lower jaw was removed, it is Kosher.

Question (against Shmuel - Rav Papa): Ikur disqualifies Shechitah!

Counter-question: How does Rav Papa understand the Mishnah?

Answer: If the Siman is uprooted from the jaw and from the flesh, this disqualifies Shechitah. The Mishnah discusses when the jaw was removed from the flesh, but the Simanim are still connected to the flesh.

Answer: Shmuel meant that most of the Turbatz Veshet was removed

Question: Shmuel taught that if most of the Simanim are dangling, it is Tereifah!

Answer: That is when they were yanked forcefully. If they were gently peeled off, it is Kosher.

Rishonim

Rif (9a): If most of the Simanim are dangling, it is Tereifah.

Rambam (Hilchos Shechitah 3:14): Ikur is when the Kaneh or Veshet or both were Nishmat before the end of Shechitah. If one slaughtered one Siman in a bird or its majority, and then the other Siman was Nishmat, it is Kosher.

Rambam (15): If one Siman was Nishmat, and then he slaughtered the other, it is Pasul. If he slaughtered one and found the other Nishmat, it is Safek Neveilah.

Rambam (9:21): If most of the Simanim are dangling, it is Tereifah, even if it is not due to falling. The same applies if they were peeled off, for they cannot be slaughtered. If most of Turbatz Veshet separated from the jaw, it is permitted, for it is not a place of Shechitah.

Rashi (9a DH Shehiyah): If one slaughtered the Veshet and broke the Kaneh, this is Ikur.

Rosh (1:13): Rashi does not discuss one who broke the Kaneh with his hand, for we would not teach that among laws of Shechitah. Rather, he broke it with a blemished knife or a reaping scythe. The nick tears, and it is as if it is broken. Bahag explains that the Siman was uprooted from its place, and then slaughtered. We say that this was taught in a Mishnah, i.e. 85a. One who does Nechirah (tears the Simanim lengthwise) or is Oker is exempt from covering the blood. If you will say that obviously Shechitah does not help, since it was uprooted and it is Tereifah, we can say that an uprooted Siman is not Tereifah. It is a tradition from Moshe from Sinai that Shechitah does not help if a Siman was uprooted from where it is attached. Even for a bird, if a Siman was uprooted from where it is attached, Shechitah of the other Siman does not help.

Rosh (1:24): It is a Safek whether we disqualify due to Chaladah or a pause after slaughtering half. The Rivam says that Hagramah and Ikur are different. If after Shechitah of the majority, Ikur occurred to the remaining minority, it is Kosher, since it is not the way of Shechitah. This is reasonable. The Rambam totally permits.

Rosh (3:6): Shmuel is Machshir when most of the Turbatz Veshet was removed. Ikur is when the Simanim were totally removed. If most of the Simanim are dangling, it is Tereifah. That is when they were yanked forcefully. If they were gently peeled off, it is Kosher. I.e. the minority that remains is still connected. If they were yanked forcefully, and the minority that remains is not connected, it is Tereifah. It will not heal.

Rashba (3:363): An uprooted Siman is not Tereifah, just the Torah permits only through Shechitah, and Shechitah is Pasul if a Siman is uprooted. If the Simanim became attached again, Shechitah would help. Surely the milk and offspring are permitted, just like they are permitted from normal animals, which are forbidden while alive.

Ran (1b DH Amar): The Ramban says that Ikur is when the Simanim were totally or mostly uprooted in a way that makes a Tereifah. A tradition from Sinai teaches that if it happened during Shechitah, it is a Neveilah, for it cannot be a proper Shechitah due to the Ikur.

Tosfos (9a DH Kulhu): Bahag explains that the Siman was uprooted and slaughtered out of (some texts - Nishmat from) its place. Why is this part of Hilchos Shechitah? Also, why do we attribute this to the Shochet? He did not do anything! In any case it is Pasul due to Hagramah! He slaughtered it after it was Nishmat. What is the Chidush? It is already Tereifah! Perhaps Bahag holds that it is not Tereifah. A tradition from Sinai teaches that Shechitah does not help.

Beis Yosef (DH veha'Ran): According to Tosfos, if the Simanim were uprooted and then it was slaughtered, it is a Neveilah. According to the Ramban, it is a Tereifah. The Rambam holds like Bahag.

Poskim

Shulchan Aruch (YD 24:15): Ikur is when the Kaneh or Veshet was uprooted from the jaw and the flesh, and one or both of them Nishmat before the end of Shechitah.

Beis Yosef (DH Ikur): Rashi explains that Ikur is a broken Kaneh. Tosfos (9a DH Kulhu) explains that he slaughtered with a blemished knife, and the Simanim were uprooted. The nick tears, and it is as if the Siman is broken. Bahag explains that the Siman was uprooted or Nishmat from its place. An uprooted Siman is not Tereifah. A tradition from Sinai disqualifies Shechitah if a Siman was uprooted. The Rosh and Rashba agreed. In a bird, if one Siman was uprooted, and the other was slaughtered, since it is not a Tereifah, the Shechitah should be Kosher! The Rashba answered that even though it suffices to slaughter one Siman of a bird, both Simanim must be proper for Shechitah (attached in their places).

Taz (8): The Shulchan Aruch connotes that if the flesh is still on the Simanim, it is Kosher. The Beis Yosef explicitly said so in the name of the Rashba. The Tur connotes that it is Tereifah if it was Nishmat from the jaw. It seems that the Rosh agrees, since he did not bring the Gemara's answer that the jaw was removed from the flesh, but the Simanim are still connected to the flesh.

Gra (Likut): The Shulchan Aruch's definition of Ikur is based on 44a. Also, Rashi is difficult, for the Gemara says that Ikur does not apply to birds, and a Mishnah (56a) teaches a punctured Veshet... (or if the majority of the Kaneh was cut). We say that Shmuel holds that Ikur does not apply to birds even regarding Shechitah.

Taz (9): The Tur says Ne'ekar or Nishmat. Ne'ekar is being uprooted through man. Nishmat is being uprooted by the animal's own motion.

Shach (21): The Shulchan Aruch holds that if flesh was uprooted with the Simanim, even if they were totally uprooted, it is Kosher.

Shulchan Aruch (ibid.): However, if one slaughtered one Siman of a bird or its majority, and afterwards the other was Nishmat, it is Kosher. If one of them was Nishmat and afterwards he slaughtered the other, it is Pasul.

Rema: Our custom is to disqualify any Ikur, whether during the first minority (of the Shechitah) or the last minority, whether of the Kaneh or of the Veshet.

Beis Yosef (DH u'Mah): The Tur is Machshir if Ikur occurred after Shechitah of the majority. The Rambam says so. Tosfos said so in the name of Rivam. Even though he disqualifies pausing, Drasah and Chaladah even in the last minority of Shechitah, Ikur does not, since it is not the way of Shechitah. The Rosh said that this is reasonable.

Shach (23): The Mechaber disqualifies only if Ikur occurred before the majority was slaughtered. Our custom is to forbid any amount of Ikur of the Kaneh or Veshet, at any time during the Shechitah, due to concern lest the Veshet was punctured. If it was Nishmat before Shechitah, we apply letter of the law. The Mechaber forbids only if it was totally uprooted from the meat of the jaw, or if the remaining minority is dangling. The Rema (below) permits the milk even when letter of the law, the animal is forbidden. It seems that this is even if the majority was dangling in its lifetime. The Tur connotes like this, and also the Ramban brought in the Ran. However, Tosfos (44a DH veha'Ika) holds that this is Tereifah even in its lifetime. The Rif and Rambam agree, and it seems that Rashi agrees. The Ro'oh agrees, and 42b proves that they are correct.

Rema: This is only after it was slaughtered. In its lifetime it is Kosher, but Shechitah will not help for it. This is relevant to its milk or eggs; they are Kosher.

Taz (10): Tosfos asked what is the Chidush of Ikur, and concluded that it is not Tereifah due to Ikur itself. The Gemara (69a) asked about milk of a Ben Peku'a (a fetus found inside a slaughtered animal) that stuck out a leg before its mother was slaughtered. Perhaps milk is permitted (and not considered Ever Min ha'Chai) only when Shechitah can totally permit the entire animal. The leg of this calf cannot be permitted! (This question was not resolved.) Even though Shechitah does not help for Ikur, the Rashba permits the milk! There, we said only that the Isur of Ever Min ha'Chai is lighter than the Isur of Yotzei, since the latter can never be permitted.