Gemara

Question (Rav Mesharshiya - Mishnah): If the baby of a Kohen (Reuven) became mixed with the baby of his slave, when the children grow up, each gives a document of freedom to the other (after Reuven dies).

(Before freeing each other,) both may eat Terumah. Together they receive one portion of Terumah at the granaries;

If a (Tahor) Bechor is born to one of them, it is left to graze. He eats it after it gets a Mum.

Gitin 41a (Mishnah - Beis Hillel): A half-slave alternates. One day he serves his master, and the next day, he keeps his earnings;

Beis Shamai: That is good for his master, but not for the half-slave! He cannot marry a Shifchah, for he is half-free. He cannot marry a Bas Yisrael, for he is half-slave.

Suggestion: He will never marry.

Rejection: "Lasheves Yetzarah" (the world was created for the sake of procreation)!

Rather, for Tikun ha'Olam, we force his master to free him, and the half-slave writes a document obligating himself to pay half his value to his master.

Beis Hillel retracted, and agreed to Beis Shamai.

Yevamos 100a (Mishnah): If they freed each other...

Question: Why is this optional? If they do not free each other, they cannot marry a slave or a Bas Yisrael!

Answer (Rava): The text should say (alternatively - it means that) we force them to free each other.

Yevamos 66a (Rav Acha bar Rav Ketina): A case occurred in which Rabanan forced the owner of a half-Shifchah to free her.

(Assumption: This was so she could marry and have children!)

Rejection: She is not commanded about Peru u'Rvu. They made him free her because men were freely having Bi'ah with her.

Kesuvos 11a (Rav Huna): If a minor wants to convert, we immerse him (to convert him) on the volition of Beis Din.

Question: A Mishnah already teaches that Zachin l'Adam she'Lo b'Fanav (we may do something purely beneficial for a person in his absence)!

Answer: One might have thought that conversion is not Zechus for a Nochri, for he prefers immorality. We hold that a slave prefers immorality!

Rav Huna teaches that this applies only to an adult, who has tasted immorality. A child has not, so conversion is Zechus for him.

Rishonim

Rambam (Hilchos Isurei Bi'ah 12:15): If the baby of a Yisrael became mixed with the baby of a slave, both of them are Sefekos. Each of them is a Safek slave. We force the Shifchah's owner to free both of them. If the son (mixed with thsv) owned the slave, when they mature they free each other, and they may marry Yisre'elim.

Rada (R. David Idan, in Likutim in Frankel Rambam): If the master had other sons, they must free the Sefekos, and then the Sefekos free each other.

Note: He says that the other children must free the Sefekos before they free each other. It is not clear to me why.

Rambam (16): If the mixed-up children were girls, each is a Safek Shifchah. Their children are Safek slaves.

Magid Mishneh: The Rambam connotes that we do not force the master to free them. The Gemara said that we force one to free a Safek slave, i.e. a male, due to Bitul of Peru u'Rvu, since he cannot marry a slave or Yisraelis. A woman is not commanded about Peru u'Rvu. A Safek Shifchah has the same law as a half-Shifchah. We do not force her master to free her (Hilchos Avadim 7:7). Surely the master cannot force them to work, for ha'Motzi mi'Chavero Alav ha'Re'ayah. Each can dispel him (and say 'I am free').

Question (R. Yitzchak ha'Levi, in Ohr Yakrus in Likutim in Frankel Rambam): Why does the Magid Mishneh say that we do not force the master to free females, just like the case of a half-Shifchah? There is different, for there is an Isur Aseh "l"Olam Bahem Ta'avodu" to free slaves without reason. Here there is no Isur, for in any case he cannot make them work. We force him to free them, for it is Midas Sedom not to. (They benefit through freedom, and he does not lose.)

Answer (Ohr Yakrus): This is not Midas Sedom, for perhaps one will sell his Zechus to the other.

Note: It seems that he means that one of the Sefekos (Ploni) will sell himself to be the Eved Ivri of the other. Then, the master can Ploni to work (like an Eved Ivri), for Ploni is either the master's Eved Kena'ani, or he is the Eved Ivri of the master's Eved Kena'ani, and a master acquires whatever his Eved Kena'ani acquires.

Magid Mishneh: If both of them were his daughters, e.g. he had relations with his Shifchah and the daughter became mixed with his daughter (from a Yisraelis), in any case he may force his daughter to work.

Ohr Yakrus: The same applies if the daughter of his slaves became mixed with his own daughter!

Note: In this way, we need not say that he transgressed relations with a Shifchah. (And also, some say that surely he freed her first to avoid the Isur!) He can force them to work only until Bagrus, for after that he does not own his daughter's earnings.

Rambam (ibid.): Similarly, if a Nochri child became mixed with a Yisraelis' child, we immerse both of them for conversion, and each is a Safek convert.

Magid Mishneh: If the child is a female, even after (Safek) conversion she is forbidden to Kehunah.

Rambam (Hilchos Avadim 7:7): If one is a half-slave, since he cannot marry a Shifchah and not a Bas Yisrael, we force his master to free him. The half-slave writes a document obligating himself to pay half his value to his master. This refers to a man, who is commanded about Peru u'Rvu. A (half)-Shifchah remains in this status, and alternates; she serves her master one day, and works for herself one day.

Poskim

Shulchan Aruch (EH 16:5): If the child of a Yisraelis became mixed with the baby of a slave, both of them are Sefekos. Each of them is a Safek slave. We force the Shifchah's owner to free both of them. If the son owned the slave, when they mature they free each other, and they may marry Yisre'elim.

Gra (13): The Gemara mentioned a Kohenes only due to the other matters, but regarding Nisu'in the same applies to a Yisraelis.

Shulchan Aruch (6): If the mixed-up children were girls, each is a Safek Shifchah. Their children are Safek slaves. Similarly, if a Nochri child became mixed with a Yisrael child, we immerse both of them for conversion, and each is a Safek convert.

Bach (DH v'Chol): A Safek convert may not marry a Mamzeres. Also, (if he married a convert - Beis Shmuel 8 cites the Bach and omits these words), his daughter cannot marry a Kohen. Also, a convert is Pasul (from being a judge) for Chalitzah.

Gra (16): Yevamos 66a teaches that we do not force one to free a half-Shifchah (and the same applies to a Safek Shifchah).

Gra (17): Kesuvos 11a teaches that we immerse a minor to convert him.