R' Heshi, it is wonderful to hear from you again after a long time! I hope you are all doing well.

1) I found that the Sefer Shevo v'Achalamah on Maseches Yevamos writes that if a Kohen found a Mes Mitzvah and buried it, or he became Tamei in a war, we send Terumah to him just as we do for the Arel whose brothers died from Milah, since this is a big Ones.

2) I saw a Peshat from Rav Chaim Kanievsky zt'l, according to which it may be that even if the Kohen was Tamei to a Mes Mitzvah, we still do not send Terumah to his house.

a) The Rambam (end of Perek 12 of Hilchos Terumah) lists the ten categories of people to whom Terumah is not given in the Beis ha'Geranos, and concludes: "But one sends Terumah to the houses of all these categories... with the exception of a Kohen who marries a woman forbidden to him, a Tamei, and an Arel, to whom we do not send Terumah at all."

b) The Kesef Mishneh asks that the Rambam appears to be contradicted by the Gemara, since the Gemara states that we do send Terumah to an Arel because he has a greater Ones than others (since his brothers died of Milah).

c) Rav Chaim Kanievsky zt'l, in Derech Emunah (Hilchos Terumos, end of Perek 12, Bi'ur ha'Halachah DH veha'Arel), answers that it is possible that the Rambam has a different Pshat in the conclusion of the Gemara, "Hai Nafish Onsei v'Hai Lo Nafish Onsei." The reason why the Arel has a big Ones is because he will never be able to be circumcised. Therefore, it is unnecessary to say that we do not send Terumah to his house. In contrast, when the Gemara states that the Tamei does not have a big Ones, this means that he will later on become Tahor. Therefore, one might have thought that we send him Terumah now since later on he will be able to eat it, and therefore the Beraisa teaches us that even so we do not send him Terumah now.

d) We learn from the Derech Emunah that there is another possible way of learning what the Gemara states, "Nafish Onsei." It means that he will never be able to eat Terumah, while "Lo Nafish Onsei" means that his inabilty to eat Terumah is only temporary. According to this, even in a case where he became Tamei due to a Mes Mitzvah it would still be termed "Lo Nafish Onsei," since later he can become Tahor, so we would not send Terumah to his house now.

3) I can give another answer to this question based on what I found, bs'd, in the Talmud Yerushalmi, Maseches Nazir 9:3 (the Mishnah there is discussing somebody who found a Mes Mitzvah). Rebbi Zeira said, "She'Ein Mesei Mitzvah Metzuyin" -- a Mes Mitzvah is not a frequent occurrence.

Therefore, we would not expect our Gemara to ask about a case where he became Tamei due to a Mes Mitzvah, since this is an unusual occurrence.

4) Now, for a Kohen to be Metamei to a Mes Mitzvah is even more unusual.

See the Gemara above (end of Yevamos 89b) which tells us that if the person who found the body can call out and people will answer him, this is not considered a Mes Mitzvah. The Shulchan Aruch (YD 374:3) writes that if there are Yisraelim near where the body was found who will answer the call of the Kohen, the Kohen is not allowed to be Metamei.

So the Mes Mitzvah would have to be located in an isolated place where the Kohen found it, and this is even more unusual, so the Gemara would not ask about such a case.

5) A different question could have been asked about a Kohen becoming Tamei to close relatives:

I told a friend about this question and my answer that a Mes Mitzvah is unusual, and he agreed but pointed out that the question could be asked: Why did the Gemara not talk about a case where the Kohen became Tamei to one of the seven close relatives about whom the Torah tells us, at the beginning of Parshas Emor, that it is a Mitzvah for him to be Metamei when they die? This is a more frequent scenario, so the answer I gave for Mes Mitzvah would not work.

However, I think that we can cite the Maharshal in Yam Shel Shlomo here (#12), who writes that the Tamei who does not send the Terumah to his house is "not a total Ones because he should have been more careful." This certainly suggests that if the Kohen became Tamei to close relatives, we would send Terumah to his house, since the Gemara (Zevachim 100a) states that if the Kohen does not want to become Tamei to his wife who died, we force him to become Tamei.

6) In my very first answer above I cited a Sefer who writes that if a Kohen becomes Tamei in a war (by touching a corpse) we still send Terumah to his home. I want now to question this and to argue that a Kohen should not go to fight in a war if he has a way of getting out of this, so if he did become Tamei in the war, it would be considered that he was not being careful enough, and we would not send him Terumah.

a) Possibly my chief source for saying this is the famous Rambam at the end of Hilchos Shemitah v'Yovel (13:12) who writes that the reason why the tribe of Levi did not receive an inheritance in Eretz Yisrael is because they were separated to serve Hash-m and to teach Torah to Klal Yisrael. The Rambam writes, "Therefore, they were separated from the ways of the world and do not wage war like the remainder of the Jewish people." Of course, Kohanim are a part of Shevet Levi, and are on a higher level than the rest of the Shevet, so since none of the Leviyim go to war, the Kohanim certainly do not go. They possess an even greater mission to teach Torah, as the prophet Malachi (2:7) tells us, "... for the lips of the Kohen shall keep knowledge and they will seek the Torah from his mouth."

b) There may be a question on the Rambam from the Gemara in Kidushin 21b which asks, is a Kohen allowed to marry a Yefas To'ar? Now, a Yefas To'ar is a special Heter which applies only in wartime, so this seems to suggest that a Kohen could go to fight in the war! I want to answer this question very simply and suggest that ideally the Kohen should not go to war but sometimes it happens that he does, so the Gemara Kidushin asks if he is allowed to marry a Yefas To'ar.

c) I think I have a second, strong source for claiming that a Kohen should not go to war. This is from the Mordechai at the end of the Perek 7 of Gitin (#432). He first writes that a few Kohanim went out to the wars of the House of David (mentioned on the first line of Kesuvos 9b). Then he writes that there must have been at least one Kohen in the war in order to read out the verse (Dvorim 20:8) " Who is frightened and of a weak heart?" in front of the army. The Mordecai concludes that it is possible that after the Cohen Moshuach reads out the verses, he then went home and did not actually get involved in the fighting.

d) The conclusion of the Mordecai seems to be that it is possible that not a single Cohen actually fought in the war. I suggest that one of the reasons for this was in order to prevent the Kohen from becoming Tamei to a dead body in the war. The Torah wants the soldiers in the war to be from tribes other than Shevet Levi, and certainly should not be Kohanim, who are the holiest of Shevet Levi. Therefore, if a Kohen did go and fight in the war for some reason and then touched a corpse and became Tamei, this is included in what Rashi (Yevamos 100a, DH Chutz) writes, that we give a fine to the Kohen since he was not sufficiently careful and we do not send Terumah to his house.

Dovid Bloom