Yevamos, Chapter 11, Mishnah 5. The Mishnah deals with another case of mix-up that could occur: "Kohenes shenis'arev v'ladah bivlad shifchasah" - the wife of a kohen whose son became mixed up with the son of her Canaanite maidservant. The maidservant's son is a slave, and the kohen's wife's son is a kohen, and we do not know which is which. The halachos that emerge from this are especially interesting, and we will go through them one by one.
As long as they have not been freed:
"Harei eilu ochlin biterumah" - both of them eat Terumah, since the slave of a kohen also eats Terumah, not only the kohen himself.
"V'cholkin cheilek echad bagoren" - when they come to the threshing floor, the place where kohanim receive Terumah, they take only one portion, since only one of them is a kohen entitled to a share; and a slave is supported from his master's portion and does not take a portion of his own.
"V'einam mitam'in l'meisim" - a kohen's slave is permitted to become tamei through contact with the dead while a kohen is forbidden, and since it is unknown which is which, both of them are stringent with themselves like a kohen and do not come into contact with a corpse.
"V'ein nos'in nashim, bein k'sheiros bein p'sulos" - a slave may marry a maidservant and is forbidden to marry a Jewish woman, while a kohen and a Yisrael are forbidden to marry a maidservant. Since their identity is unknown, there is no woman whom they may marry.
Regarding the division at the threshing floor, a precise reading is called for: on the face of it, it is obvious that only the kohen takes a portion and the slave eats from that very same portion, and the Mishnah is teaching nothing new. Rather, the Mishnah comes to teach us that since it is unknown which of them is the kohen, both of them must come together, for Terumah is not given to a slave unless his master is with him. Otherwise, people might think that he is the kohen and permit him to marry a Jewish woman - which is forbidden to him - or say that his children are of valid lineage and that his daughters are fit to marry a kohen. But when he comes together with his master and they take only one portion, it is clear to everyone that one of them is a slave.
Once they grew up and freed one another:
Once the two who were mixed up grew up, we compel them to free one another: each one says to his fellow, "If you are my slave - you are hereby freed," and the second does the same. From now on the status of both of them is that of a Yisrael, since one of them is a kohen and the other is a freed slave. And these are the halachos that apply to them:
"Nos'in nashim har'uyos lakehunah" - now they may marry, but they may marry specifically women who are fit for kehunah, since perhaps one of them is a kohen.
Tumah of a corpse: they still do not become tamei through contact with the dead, but if they did become tamei - there is no punishment and they do not receive lashes for the prohibition of a kohen coming into contact with a corpse, since each of them claims: I am not necessarily a kohen.
"V'ein ochlin biterumah" - once the slave has been freed he no longer eats Terumah, since he ate only by virtue of being the slave of a kohen, and therefore neither of them eats.
"V'im achlu - ein meshalmin keren v'chomesh" - a Yisrael who ate Terumah unintentionally pays the kohen the principal plus a fifth, and here they do not pay this penalty, since each of them claims, "I am a kohen." (It should be emphasized that we are speaking of one who ate Terumah unintentionally.)
"V'ein cholkin al hagoren" - they do not take a portion of Terumah at the threshing floor, even though one of them is certainly a kohen and they come together, out of concern that they might come to eat from it.
Selling the Terumah: the Terumah that they themselves separate they may sell to kohanim, and the money is theirs, since in monetary matters they claim: bring proof that I am not a kohen.
"V'ein cholkin lahem b'kodshei mikdash" - they are not given a portion in the meat of the sacrifices, nor in the hides of the sacrifices, for the kohanim say to them: bring proof that you are a kohen - since this too is a monetary matter. Likewise, they do not perform the service in the Mikdash, since perhaps they are not kohanim.
Some explain that this applies as well to the giving of a cherem, which is given to a kohen and is a monetary matter, for it is obvious that they are not fit to offer sacrifices. And if they themselves became obligated in a korban - a chatas, an asham or an olah - they are not compelled to hand it over to the men of the mishmar, the group of kohanim assigned to serve that week, as we would say regarding a Yisrael. For there is monetary value involved - who will merit to offer that korban - and they claim: since I cannot offer it myself, as perhaps I am a kohen, I may give it to any kohen I wish, and you cannot obligate me to give it specifically to the men of the mishmar.
The Mishnah further states: the foreleg, the cheeks and the maw, which are the priestly gifts that a Yisrael who slaughters an animal must give to a kohen - they are not obligated to give them. These gifts carry no sanctity and even an ordinary Yisrael eats them, and in monetary matters they claim: prove that I am not a kohen and then I will give, and in the meantime I hold on to what is mine.
So too the firstborn animal of each of them - it grazes until it develops a blemish, since once it has a blemish even a Yisrael may eat it, and therefore they may keep it.
"Nosnim aleihem chumrei kohanim v'chumrei Yisre'elim":
The Gemara asks: to what does this refer? And it explains that this refers to a minchah that they bring in the Mikdash. In the minchah of a Yisrael, the kohen takes a handful and offers it on the altar, and the remainder is eaten by the kohanim; whereas the minchah of a kohen is burned in its entirety. And since it is unknown whether they are kohanim, we apply both stringencies to them at once: the handful is taken and the kohen offers his full handful on the altar, but the kohanim do not eat the remainder, out of concern that it may be the minchah of a kohen, from whose remainder it is forbidden to eat. The result is that the handful is offered on the altar, and the rest is burned in the beis hadeshen, the place where disqualified offerings are burned.
In summary: in this Mishnah we learned the law of the son of a kohen's wife and the son of her maidservant who became mixed up with one another. As long as they have not been freed - both eat Terumah and take one portion at the threshing floor when they come together, they do not become tamei through contact with the dead, and they do not marry at all. Once they grew up and freed one another - they marry women who are fit for kehunah, they do not become tamei but are not punished if they did, they do not eat Terumah and do not pay the principal plus a fifth, they do not take a share at the threshing floor or in the sacrifices of the Mikdash, while the Terumah they separated, the priestly gifts and the firstborn animal they keep in their possession by virtue of the rule that in monetary matters the burden of proof is upon the claimant. Finally, we saw the combination of the stringencies of kohanim and the stringencies of Yisraelim in their minchah - taking a handful as in the minchah of a Yisrael, and burning the remainder as in the minchah of a kohen.