Gemara

(Beraisa - R. Meir): A nursing woman does not normally see Dam Nidah because her (menstrual) blood turns to milk.

Bechoros 6b: According to R. Meir, blood (of a nursing woman or animal) is converted into milk. It is a Chidush that milk is permitted. R. Yosi disagrees. However, also he requires a source to permit milk, for normally, anything that comes from a living being is forbidden.

"Eretz Zavas Chalav u'Devash" teaches that milk is permitted. Eretz Yisrael would not be praised for something forbidden to eat!

Temurah 30b (Beraisa - R. Chanina ben Antigionus): If a Kosher calf nursed from a Terefah, it may not be offered.

Suggestion: This is because it was fattened by the Tereifah's milk.

Rejection: If so, we should forbid an animal that ate vetch of idolatry!

(R. Chanina Trita'ah): Rather, he forbids a calf that nursed (from a Tereifah) every morning, for this is enough to sustain it.

31a (Abaye): All permit a chick that comes from an egg of a Terefah. Before it develops, it putrefies, so it is like earth (the Isur goes away).

Rishonim

Rambam (Hilchos Isurei Mizbe'ach 3:14): An animal fattened with vetch of Isur is permitted to the Mizbe'ach, for it (the vetch) changed.

Perush ha'Mishnayos and Bartenura (Temurah 6:5): The Mishnah forbids a Kosher animal that nursed from a Terefah only the day it nursed, for the milk can sustain it for 24 hours, and digestion is not finished until 24 hours. After it was digested, even if it was fattened excessively with vetch of idolatry, all permit it. The Halachah does not follow R. Chanina.

Rosh (Berachos 6:35): Something like blood gathers in the throat of a certain Chayah, and becomes musk. R. Yonah permits, for perhaps it is a mere Pirsha (secretion). Even though initially it was blood, we are not concerned. It depends on what it is now. This is like Isur that dissolved in honey. It is transformed to honey, so we permit it like honey. R. Yonah's proof needs a proof.

Tosfos (31a DH she'Yankah): Likewise, if an animal ate vetch of idolatry it is forbidden, for it grew primarily from Isur. It seems that it is forbidden even to people.

Piskei Tosfos (20): If a Kosher animal nursed from a Terefah, it is Pasul for the Mizbe'ach and Kosher to people.

Mordechai (Yevamos 65): If a Kohen rented a cow from a Yisrael, even though he must feed it, he may not feed it vetch of Terumah. R. Yakir explains that if one would feed and fatten it through Terumah, (after it is slaughtered) the Yisrael who eats it would eat Terumah. This is difficult. If so, why may we eat chickens fattened through eating Sheratzim?

Poskim

Rema (YD 60:1): If a (Kosher) animal was fattened with Isur, it is permitted, unless it was fed only Isur its entire life.

Shach (5): One may feed his animal Isur that is Mutar b'Hana'ah, for one does not eat the Isur itself. Tosfos (Avodah Zarah 49a DH she'Im) connotes like this. In Klal 47 also Isur v'Heter permits, for digestion is like burning.

Machazik Berachah (of the Birkei Yosef - 2): We can challenge R. Yakir from Temurah 30b. The Mishnah connotes that R. Chanina ben Antigionus forbids a Kosher calf that nursed from a Terefah, but Chachamim permit, and the Halachah follows them. Perush ha'Mishnayos and the Bartenura explain like this. Just like a calf that nursed from a Terefah is Kosher to the Mizbe'ach, an animal that ate Terumah is Kosher (even to Yisre'elim). I answer that R. Yakir holds that Chachamim are Machshir b'Di'eved. They argue about l'Chatchilah. It may not nurse from a Terefah, and a Yisrael's animal may not eat vot, for this fattens it, so it is as if the Yisrael eats Terumah. The Mordechai disagrees and holds that Chachamim permit l'Chatchilah. We learn from chickens, which get fat from Sheratzim. This is like l'Chatchilah. Indeed, it is clear from Piskei Tosfos that Tosfos (31a) rules like R. Chanina ben Antigionus, and also the Agudah does. Since the Gemara discusses his opinion, this implies that the Halachah follows him. The Rambam and Bartenura hold that the Gemara merely sought to understand his opinion, so the rule that 'the Halachah follows the opinion that the Gemara analyzes' does not apply.

Machazik Berachah (DH v'Chazisei, citing Keneses ha'Gedolah): The Mordechai discusses chickens that occasionally eat Sheratzim, but if they always get fat from Sheratzim, all forbid, like the Mishnah of an animal that nursed (from a Terefah). The Gemara says this is when it nursed (from a Tereifah) every morning, for this is enough to sustain it. Rashi says that this is even if it ate other things in between. The Rema, Levush and Isur v'Heter (47) say so. How can R. Yakir explain the Gemara, which teaches that even R. Chanina forbids only if it nursed every morning?

Machazik Berachah: It is not clear how Keneses ha'Gedolah decided that the Mordechai permits only if it ate Sheratzim occasionally, and could not have survived on them alone. The Isur v'Heter says 'if one bought an animal from a Nochri and afterwards found out that it surely grew up amidst Tamei animals, there is no concern, just like chickens and doves that eat vermin. They are permitted, for the vermin is totally digested. It is as if they were burned. This applies even if they ate them every day. We infer this also from 'it became known that it grew up amidst Tamei animals.' The Shach and some Acharonim say that the Mordechai and Isur v'Heter permit even if it ate Isurim its entire life. The Rema holds that the Mordechai argues with Tosfos, and he rules like Tosfos. Some cite the Mordechai to be the source for the Rema's law. They err:

Question (Magen Avraham 216:3): R. Yonah permits musk (and Isur mixed into honey), because it becomes Heter. This is difficult, for in Bechoros, we say that milk is a Chidush, since it came from blood. This shows that it depends on the origin! We do not learn from a Chidush! Do not say that musk is a mere Pirsha, and not a food. If so, all would permit it, just like all permit curdling in (milk in the) stomach of a Kosher animal that nursed from a Tereifah. R. Yonah said that it is a mere Pirsha only to teach that is not blood. We permit a chick that hatches from a Tereifah egg, for until it spoils, it does not develop. When it (starts to) develop, it is like mere dirt. If not for this, it would be Asur, like its origin!

Answer Chak Yakov (OC 467:16): R. Yonah says that if meat or Neveilah dissolved in honey, it is transformed to honey. The law depends on its current status. One may not rely on this, like the Rosh and Shirei Keneses ha'Gedolah say. It is unlike the Yerushalmi. The Chidush of milk does not disprove R. Yonah. One might have thought that it is totally forbidden, for it comes from blood, so it is still like blood, even though its appearance changed. It did not change to Heter. If Isur put in honey turns to honey, it changed to Heter. Why should it be unlike other honey? It has the same taste and appearance. With difficulty, one could say the same for musk.

Igros Moshe (OC 1:147 Anaf 7 DH v'Hinei): R. Yonah says that if Isur fell into honey, it is permitted, because it is transformed into honey. If so, if an animal was fattened through Isur, it was transformed into a Tahor animal. The Magen Avraham asked from Bechoros, which says that it is a Chidush that the Torah permitted milk, because it comes from blood. We permit a chick that hatches from an egg of a Terefah, because before it is born it became mere earth. This shows that we follow the initial state (unless a verse teaches otherwise). Chak Yakov answered only regarding honey, but not regarding musk. I answer that R. Yonah holds that if an Isur changed to another name, it is as if the Isur was burned and it is not in the world at all. There is only the new name, which is Heter. However, we should still forbid because 'what comes from Isur is Asur.' This is only when the change came from the Isur itself, e.g. a chick from an egg or milk that comes from blood. The birth, milking and nursing caused the blood to be thickened, and then it itself changed to milk. Therefore, even though it is a new matter, it came from Isur. All the more so this applies to a chick, which develops from the egg's own heat. Therefore the Torah needed to permit these. If the change came from the outside, e.g. from honey, the Isur is just a Gorem. We do not say that the result came from Isur. R. Yonah holds that digestion changed the food to Peresh. It is forbidden because it came from Isur. The Isur did not cause digestion, rather, the body did. Therefore, it is not considered something that comes from Isur. Blood turns to musk only in a certain place (a hump in the neck), therefore it is not considered something that comes from Isur. If one planted forbidden seeds, we do not say that what grows comes from Isur, because they (degenerate and) sprout only in the land. Surely, if man changed an Isur through a machine, it is still forbidden, for it is not natural.

Igros Moshe: According to R. Yonah, an animal fattened through Isur is permitted, for digestion is natural. It is not recognized that the improvement comes from Isur, since it would have become fat through eating anything. This is unlike a chick, which could not have come from any other egg. Also, milk or the chick in this egg can only come from Isur (from blood, or the egg of a Terefah). Honey need not come from Isur, and an animal need not eat Isur, therefore the result is not attributed to the Isur. Seemingly, we can prove this from a Tamei animal that ate Heter, The entire animal is forbidden. One is lashed for eating exactly a k'Zayis. The Heter food it ate became Isur. Likewise, if a Tahor animal ate Isur, it becomes Heter. However, this is wrong. A Tamei species is forbidden even if it came totally from Heter, e.g. worms that (spontaneously) arise in fruits. However, the law is correct.