Gemara

There are 15 Arayos that exempt their Tzaros from Yibum or Chalitzah...Chamoso (his mother-in-law)...

Sanhedrin 76b - Beraisa - R. Yishmael: "(V'Ish Asher Yikach Es Ishah Es Imah...) Oso v'Eshen" - (if a man married a woman and her mother,) he and one of them (the one he married last) are killed;

R. Akiva says, he and both of them are killed.

Question: What do they argue about?

Answer #1 (Abaye): They agree about the Halachah. They argue about how to derive it:

R. Yishmael expounds that we burn 'Oso' (him) and 'Eshen' (one of them). In Yevani, 'Heinah' means one. The verse does not explicitly discuss the mother of Chamoso. Rather, we expound it.

R. Akiva says, Eshen refers to both of them, Chamoso and her mother.

Answer #2 (Rava): They argue about the Isur of Chamoso after the wife died:

R. Yishmael learns from "V'Eshen" that even if only one of them is alive (i.e. his wife died), Chamoso is killed;

R. Akiva says that Chamoso is killed only if both of them are alive. If not, it is a mere Isur.

Yevamos 98b - Beraisa - Version #1: If a Nochri's wife died, (after conversion) he is permitted to his mother-in-law.

Version #2: He is forbidden to her.

The latter opinion is like R. Yishmael, who says that the Isur of Chamoso is the same after the wife dies. Chachamim decree regarding a convert;

The former opinion is like R. Akiva, who says that the Isur becomes lighter after the wife dies. Chachamim did not decree regarding a convert.

Rishonim

Rashi (Yevamos 2a DH Chamoso): Reuven's father-in-law died, then his mother-in-law married Reuven's brother Shimon. Shimon died, and Reuven's mother-in-law fell to him to Yibum.

Question: Why didn't Rashi explain more simply, that Reuven married Shimon's daughter, and then Shimon died childless, i.e. after his daughter died?

Answer #1 (The questioner in Teshuvas Rivash 374): This shows that Chamoso after the wife died is not an Ervah that exempts from Yibum and Chalitzah.

Rejection (Rivash, ibid.): R. Yishmael says that even after the wife died Chamoso exempts from Yibum and Chalitzah, but R. Akiva disagrees. Our Tana did not discuss cases about which Tana'im argue (9b). Also, the Gemara says that there is Sereifah for Chamoso. This shows that (if it is like R. Akiva) the wife is still alive.

Answer #2 (Maharam DH Masnisin): Rashi could also have explained that Reuven married Shimon's daughter, and then she died and then Shimon died.

Rashi (Sanhedrin 76b DH R. Akiva): R. Akiva holds that after the wife died there is no Chiyuv Misah for Chamoso. The curse "Arur Shochev Im Chosanto" applies.

Me'iri (98b DH Kevar): Rashi says that there is no Misah, implying that there is Kares.

Maharshal (Yevamos 94b DH me'Isura): 'A mere Isur' connotes that there is no Lav. Rashi holds like this.

Rambam (Hilchos Isurei Bi'ah 2:7): When a man is Mekadesh a woman, he becomes permanently forbidden to six relatives, i.e. her mother, the mothers of her mother and father, her daughter, and the daughters of her son and daughter.

Rambam (8): If he has relations with one of them after his wife died, the punishment is Kares but there is no Misas Beis Din. It says "Oso v'Eshen" - there is Sereifah only if both of them are alive.

Magid Mishneh: The Halachah follows R. Akiva against a colleague. Even though R. Akiva says that it is a 'mere Isur', this means that there is no Misah, but there is Kares. The other relatives of the wife are learned from Chamoso. We cannot say that there is Misah for them after the wife died; Dayo (it is enough) to be as stringent about them as for Chamoso. Many argue with the Rambam and say Dun Minah v'Uki b'Asra (we only learn one law from the source, other laws are according to the law of the matter being learned. We learn Sereifah for five other relatives of his wife from Chamoso, but we apply to them the law of other Arayos, that the punishment never changes.)

Rambam (14:15): If a man married a convert and she died, he may marry her mother or daughter. Chachamim decreed to forbid this only in the life of his wife.

Rosh (Yevamos 11:2): R. Chananel rules like R. Yishmael, therefore if a Nochri's wife died, he is forbidden to his mother-in-law. Others rule like R. Akiva according to Rava.

Nimukei Yosef (32a DH Mesah Ishto): The case is, he and both women converted before his wife died. Letter of the law, Chamoso is permitted. We are not concerned lest people say that conversion was a descent in Kedushah, for she was permitted before conversion. Rather, the concern is lest Yisraelim err and do similarly. "Arur Shochev Im Chosanto" includes the wife's grandmothers. Also regarding these R. Akiva holds that the Isur is lighter after the wife died.

Or Some'ach (Isurei Bi'ah 2:8): All agree that there is Kares for the daughter and granddaughters of one's wife even after the wife died. Rava (22b) asked a contradiction between "Ervas Bas Bincha...", which implies that your wife's granddaughters (that are not from you) are permitted, and "Ervas Ishah...Es Bas Benah ..."! To answer this he distinguished between granddaughters that came (from children) through wedlock and those not through wedlock. He did not say that her granddaughters not from you are forbidden (with Kares) only in her lifetime!

Tosfos (98b DH Mutar): Even though R. Akiva agrees that there is Kares even after the wife dies, since the Isur is lighter (there is no Misah) Chachamim did not forbid. Abaye holds that all agree that there is still Misah. He must deny that a version permits the mother-in-law.

Poskim

Shulchan Aruch (YD 269:6): If a man married a convert and she died, he may marry her mother or daughter. Chachamim decreed to forbid this only in the life of his wife.

Shach (10): Some forbid even after his wife died. The Tur is stringent.

Question (Noda bi'Yehudah EH 2:148, partially cited in Pischei Teshuvah EH 173:2): Why don't the Poskim discuss the Isur of Chamoso after the wife died? According to the Rambam, there is still Kares, so Kidushin does not take effect. According to the Ramban and Rashba (Yevamos 98b), there is not even a Lav, only an Isur Arur, so Kidushin takes effect!

Answer (Noda bi'Yehudah, ibid.): Perhaps the Halachah follows R. Yishmael, like the Rosh says in the name of R. Chananel. And even if the Halachah follows R. Akiva, perhaps R. Akiva agrees that there is Kares after the wife died, like the Rambam says. Therefore we are not concerned for Kidushin or Zikah (to require Chalitzah), because there is a Sefek-Sefeka (two doubts). However, if one married a convert, after she dies he may marry her mother because this is a Safek about a mid'Rabanan law (perhaps the Halachah follows R. Akiva).

Note: Tosfos (Bava Kama 11a DH d'Ka) says that we cannot be lenient about a Sefek-Sefeka (perhaps A is true, and even if A is false perhaps B is true) if there is another 'opposite' Sefek-Sefeka (perhaps A is false, and even if A is true perhaps C is true). It is illogical to be lenient about one of these and stringent about the other, and we cannot be lenient about both because this is Tartei d'Sasrei (contradictory). Either the Noda bi'Yehudah disagrees, or he holds that Tosfos' principle applies only to mid'Oraisa laws.

Conclusion (Noda bi'Yehudah ibid., DH va'Ashuvah): We should be stringent about Chamoso (a convert) after his wife died because R. Chananel rules like R. Yishmael. On the other hand it is difficult to ignore Zikah, because the Sugya seems to prove that the Halachah follows R. Akiva.

R. Akiva Eiger (Teshuvah 121): The Shulchan Aruch permits even the daughter (a convert) of one's deceased wife. This is surprising, because only the Rambam holds that a step-daughter becomes more lenient after the wife died. Further, the Shulchan Aruch is not concerned for Kidushin of a mother-in-law after the wife died, even though many Rishonim holds that this is only Chayavei Lavin!