Gemara

39b (R. Zeira): If a slave married a Bas Yisrael in front of his master, he goes free.

Question (R. Yochanan - Beraisa - R. Meir): If a man wrote a document of Kidushin to his Shifchah, she is Mekudeshes;

Chachamim say, she is not Mekudeshes.

Answer: Rabah bar Rav Shilo taught that a slave is free if his master himself put Tefilin on the slave. Here, he goes free if the master himself married off the slave.

Question: Do Chachamim hold that the master would not cause his slave to sin, but he himself would sin (by marrying his Shifchah without freeing her)?

Answer (Rav Nachman bar Yitzchak): The case is, he told her that the document should free her and be Mekadesh her to him. The Tana'im argue about whether or not 'you are Mekudeshes to me' is a valid expression of freedom.

Yevamos 22a (Mishnah): A son from any mother exempts his father's wife from Yibum and Chalitzah. The only exceptions are a son from a Shifchah or Nochri.

Kesuvos 72b (Rav): If a man was Mekadesh a girl on Tanai (conditionally) and did Nisu'in with her Stam (and the Tanai was not fulfilled), she needs a Get from him (before she can marry someone else);

(Shmuel): She does not need a Get.

(Abaye): Rav does not hold that since he did not mention the Tanai at the time of Nisu'in, this shows that he pardoned it. Rather, a man avoids Bi'as Zenus.

Rishonim

Rif and Rosh (Yevamos 5a and 2:3): The Mishnah says that a child from a Shifchah or Nochris does not exempt from Yibum and Chalitzah. Rabanan say that just like the Nochris is not his own, also the Shifchah. However, if one had Bi'ah with his own Shifchah, even though she does not have a Get Shichrur, the child is his. A man avoids Bi'as Zenus. (Surely, he freed her before Bi'ah.) If he has Bi'ah with her daughter from him, he is liable for Bi'ah with his own daughter. A Gaon was unsure about this. He is stringent about Isur to require Chalitzah. He is lenient about money; the Shifchah's son does not inherit, but the heirs may not sell him. The son may not marry a Bas Yisrael without a Get Shichrur.

Question (Ben Lev, brought in Lechem Mishneh Hilchos Nachalos 4:6): If the master has no other sons, the Shifchah's son should inherit half, for perhaps he is the sole heir!

Answer #1 (Ben Lev): The Rif discusses when the master has other sons. They Vadai inherit and the Ben Shifchah is Safek. A Safek cannot take from a Vadai.

Answer #2 (Lechem Mishneh): Even if he is the only son, since we saw that he is a Ben Shifchah, his Chazakah is worse. He is considered a Safek compared to the other heirs.

Rosh: R. Natrunai Ga'on learns from Gitin 39b. Even Chachamim agree that a man does not sin and he intended to free her, just he erred about what is a valid expression of freedom. Therefore, one who had Bi'ah with his Shifchah, whether it was like marriage or like Bi'as Zenus, surely freed her beforehand. The Rambam disagrees. I disagree with the Rambam.

Rambam (Hilchos Nachalos 4:6): If Levi fathered a child from his Shifchah and treated him like a son, or said that he is his son and his mother was freed:

If Levi is a Chacham or is established to observe Mitzvos meticulously, the son inherits him. Nevertheless, he may not marry a Bas Yisrael until he proves that his mother was freed before he was born, for she was Muchzekes to be a Shifchah.

Question: Also a proof that he freed the son permits the son to a Bas Yisrael!

Answer (Radvaz 1550): The Rambam teaches that when the father is not a Tzadik, a proof that he freed the mother before birth suffices for the son to inherit for several reasons. Presumably, he freed the mother before Bi'ah to avoid the Isur. The fact that he freed her later supports this. The son has a Chazakah; he was born bi'Kedushah. The father says that he is his son.

Rambam (ibid.): If Levi is a commoner, and certainly if he is one who freely has Bi'as Zenus, the son is Muchzak to be a slave in every respect. His paternal brothers can sell him. If Levi has no other children, Levi's wife may do Yibum (or Chalitzah). Some distinguish between whether or not Levi was Kosher only regarding selling the son. Some do not distinguish even regarding inheritance. One should not rely on this.

Ra'avad: There is no source for this in the Gemara. Ge'onim argue about whether or not we distinguish between his Shifchah and another's. This is only when he had Bi'ah Stam. If he testified that his mother was free, he inherits him.

Magid Mishneh (DH veha'Ra'avad): The Torah believes a man about his son, but this does not include a child from a Shifchah, who is not considered his son.

Question (Lechem Mishneh): There is a Migo to permit the son to marry a Bas Yisrael; the father could free him. Why don't we rely on this Migo, since the Chazakos offset each other?

Poskim

Shulchan Aruch (CM 279:6): If Levi fathered a child from his Shifchah and treated him like a son, or said that he is his son and his mother was freed:

If Levi is a Chacham or is established to observe Mitzvos meticulously, the son inherits him. Nevertheless, he may not marry a Bas Yisrael until he proves that his mother was freed before he was born, for she was Muchzekes to be a Shifchah.

If Levi is a commoner, and certainly if he is one who freely has Bi'as Zenus, the son is Muchzak to be a slave in every respect. His paternal brothers can sell him. If Levi has no other children, Levi's wife may do Yibum.

SMA (17): We are stringent about every Safek Isur. If the son was Mekadesh a woman, she needs a Get.

Rema: Some say that she must do Chalitzah. Some say that regarding money, ha'Motzi me'Chavero Alav ha'Re'ayah, and I agree.

SMA (18): This means that the son does not inherit, for the other heirs are Muchzakim. They cannot sell him, for he is Muchzak in himself. The Rema cites two opinions. The first is stringent only about Isur, but is lenient about money and says that the son inherits. The latter opinion considers the son to be a Safek even regarding money. The Tur says that the opinion that requires Chalitzah also considers the son to be a Safek regarding money. It is not clear what is the Rema's source to distinguish.

Shach (4): The SMA understood that the Rema brings two opinions that require Chalitzah even when the father is a Tzadik. This is wrong. He discusses when the father is immoral. The first opinion says that nevertheless regarding money we rely on the Gaon and the Ben Shifchah inherits when the master has no other sons, like the Ben Lev (brought above). The latter opinion says that even in this case the Ben Shifchah inherits, even if the father is a Tzadik.