Gemara

Version #1 (according to Rav Acha - Ameimar): If a female bird became a Tereifah, eggs that were inside at the time are forbidden;

Eggs that formed later are permitted, for we permit Zeh v'Zeh Gorem (something that comes from two sources, one of which (in this case, the father) is permitted).

Question (Rav Ashi - Mishnah): They agree that eggs of a Tereifah are forbidden, for they grew inside a forbidden bird.

Answer (Ameimar): That refers to eggs that developed without a male (the hen warmed itself in the earth).

They are due solely to the mother.

Version #2 - Ravina - (Ameimar): If a female bird became a Safek Tereifah, we hold onto eggs that were inside at the time:

If the bird later forms more eggs, all the eggs are permitted. If it does not form more eggs, the (first) eggs are forbidden.

Question (Rav Ashi - Mishnah): They agree that eggs of a Tereifah are forbidden, for they grew inside a forbidden animal.

Answer (Ameimar): This discusses eggs inside the bird when it became Tereifah.

The Mishnah should say that they were completed inside a forbidden bird.

Question: Why are they forbidden?

Answer: They are like part of the bird. (They became forbidden with it.) (end of Version #2)

Bava Kama 47a (Rava): If a pregnant cow damaged, one may collect from the calf.

This is because it was part of the cow.

If a chicken damaged, we do not collect from the eggs.

This is because it is a mere Pirshah (something that separated from it).

Beitzah (7a): If one slaughtered a chicken and found finished eggs inside, one may eat them with milk;

R. Yakov forbids if they were intertwined with sinews.

Idiyos 5:1 (Mishnah - Beis Shamai): The egg of a Neveilah or Tereifah is permitted if such eggs are sold in the market. If not, it is forbidden;

Beis Hillel forbid.

They agree that an egg of a Tereifah is forbidden, for it grew b'Isur.

Rishonim

Tosfos (Chulin 11a DH Asya mi'Parah): The Gemara wanted to prove from Parah Adumah that we follow the majority (and assume that a Stam animal is Kosher). Perhaps we do not rely on the majority, rather, on Chazakah, according to the opinion that a Tereifah cannot live more than a year! A Parah Adumah must be at least two years old (so it was Kosher at birth.) We can say that this would not suffice (for its ashes to be Metaher), for there is an opposing Chazakah, that what was sprinkled on was Tamei. However, the Gemara tries to learn that we follow the majority from Edim Zomemim. (There, the only Chazakah is that they were initially healthy.) Rather, we do not rely on any Chazakah that was never known at the time. (E.g. what is alive now was not Tereifah a year ago.) Therefore, if cheese was made from milk of several animals, and one was slaughtered and found to be Tereifah, all the cheese is forbidden. We do not say that the cow was Muchzak to be Kosher (since it was above a year, or gave birth).

Ran (19a DH Mashinan): Some say that we forbid a Tereifah egg only if we know that it was Tereifah before the Shechitah, e.g. lesions in the lungs. We cannot say that they arose at the time of Shechitah. Since it lost its Chazakah, and we do not know how long before the Shechitah, we forbid it retroactively. However, if we slaughtered it and found that it is Tereifah, and we do not know when it became Tereifah, the eggs and (in the case of an animal) milk are Kosher. We leave it in its Chazakah. We say that now it became Tereifah. However, Tosfos says that we do not rely on any Chazakah that was not known at any time. Therefore, the eggs and milk are forbidden.

Question: Our Sugya connotes that the egg is like its body. Therefore, when the bird became Tereifah, also the egg is forbidden, even if it was totally finished beforehand. We bring the Mishnah that forbids a Tereifah egg because it grew b'Isur, i.e. it finished b'Isur, like the Gemara answers. The Gemara discussed a Neveilah egg. In Beitzah (7a), it seems that even if it is intertwined with sinews, it is not like the bird. R. Yakov forbids eating them with milk finished eggs found in a slaughtered chicken if they were intertwined with sinews. This implies that Rabanan permit, for it is not like the bird itself. If a chicken damaged, we do not collect from the eggs, for it is a mere Pirshah!

Answer (Ran, ibid.): Letter of the law, eggs are a mere Pirshah. This is why Chachamim permit to eat them with milk, and one may not collect damages from them. Regarding the Torah Isur of Tereifah, Chachamim were stringent. Since they are attached to the bird, they are like its body. Sometimes they appear like part of the body, i.e. when they are intertwined with sinews. Chachamim were stringent even when they are not intertwined with sinews, even if such eggs are sold in the market.

Question: Why do Beis Hillel forbid a Neveilah egg? If one slaughtered a chicken and found finished eggs inside, one may eat them with milk!

Answer (Tosfos 58a DH v'Shavin): Bahag says that Chachamim were stringent about Neveilah, which is mid'Oraisa, and lenient about meat and milk, which is mid'Rabanan (regarding fowl). R. Tam answered that they were stringent about Neveilah, for the Isur is from it itself. The Isur of meat and milk is due to a mixture. Alternatively, they forbid a Neveilah egg due to a Tereifah egg, which is forbidden because it finished b'Isur. I disagree with the last answer. We do not decree to forbid the last litter of eggs (that formed after it became Tereifah. They are permitted due to Zeh v'Zeh Gorem) due to the first litter, or due to eggs not fertilized through a male (the egg is totally due to Isur, i.e. a Tereifah bird).

Poskim

Shulchan Aruch (YD 86:3): The egg of a Neveilah or Tereifah is forbidden, even if it was completed, and such eggs are sold in the market.

Beis Yosef (DH Beitzas): The Rashba (58a DH v'Shavin) forbids even if it laid eggs right after it became Tereifah. This is a decree due to eggs intertwined with sinews. This is unlike Orchos Chayim in the name of the Ro'oh, who permits.

Beis Yosef (DH u'Mah she'Chasav Aval): The Tur forbids a Safek Tereifah egg. This is because it is a Safek mid'Oraisa. Perhaps when `the bird became Tereifah, the egg was meat without a shell, which is like a limb of the bird, and afterwards the shell finished. Sefer ha'Terumah says so. If so, if it became Tereifah just before Shechitah, it is forbidden only mid'Rabanan, for there was no time in between to finish, so we are lenient about a Safek. It seems that even so, we consider it to be a Torah Isur. They did not fix a Shi'ur (how long afterwards the Shechitah must be to consider it a Torah Isur).

Taz (6): The Beis Yosef brings from the Rashba that even if it laid eggs right after it became Tereifah, they are forbidden. This is a decree due to eggs intertwined with sinews.

Shach (8): A Neveilah egg is forbidden only mid'Rabanan. The Torah permits, for it cannot be finished after death. The Torah forbids Tereifah eggs, for afterwards they finished b'Isur. Even if it became Tereifah just before Shechitah, the Torah forbids. It did not distinguish, like the Beis Yosef says. The Rema (Toras Chatas 71:1) agreed. See what I wrote above (79:8) and below (87:9,10).

Support (Gilyon Maharsha 6): In Beitzah (6b), Rav taught that an egg is finished just before it comes out. (The Gemara struggled to explain what this pertains to.) It did not say that he forbids mid'Oraisa an egg born to a Tereifah (even if it was born right after the bird became Tereifah! Rather, we must say that in any case the Torah forbids, even if it was finished earlier - PF.)

Pleisi (4): We cannot say that it is Asur mid'Oraisa because 'they did not distinguish.' The Rashba clearly says that if it became Tereifah just before the egg was laid, the Torah permits. Chachamim decreed to forbid, due to an egg intertwined with sinews. The Beis Yosef had a Hava Amina to be lenient about a Safek, but concluded that we do not distinguish, and consider it like a Torah Isur, and we are stringent about a Safek.

Pri Chodosh (10): Chachamim did not distinguish how long after becoming Tereifah the egg was laid. There is a textual error in the Shach. (It should say that it is forbidden mid'Rabanan. Chachamim did not distinguish.)

Sifsei Da'as (8): The Shach does not really mean that it is forbidden mid'Oraisa. Rather, we are stringent about a Safek, as if it were an Isur Torah. Chachamim did not fix a Shi'ur. This (saying that even though we are stringent about a Safek, it is mid'Rabanan) affects the status of people who transgress (to rely on them for Isurim or testimony). The Shach said 'see what I said above (79:8).' There, he said that the child of a Tereifah is Kosher because it has its own life (but an egg was finished b'Isur). This implies that the Torah forbids a Tereifah egg even if it was born right away.

Sifsei Da'as (8): If only the yolk of a Neveilah egg was finished, or it was intertwined with sinews, perhaps it is an Isur Torah. The Isur is only mid'Rabanan if such eggs are sold in the market. There are cases of living animals that are considered Neveilah (Chulin 20b, 21a). If a bird became Neveilah, and a while after laid eggs, since such a Neveilah is immediately Tamei, it is considered like a Mes, so we cannot say that the egg was laid b'Isur. This requires investigation if they are forbidden mid'Oraisa.

Hagahos (Shulchan Aruch ha'Shalem 11): In his introduction to Hilchos Shechitah (Shoresh 3, DH Emnam, the sixth distinction) the Pri Megadim himself said that surely, the Torah forbids them.

Pischei Teshuvah (1): The Levushei Serad (14) said that there is no Safek. Surely it is totally like a Neveilah egg. He also said that if the Veshet was punctured or the Kaneh was cut, the Torah forbids the egg.