Gemara

17b (Rav Huna citing Rav): If a Yevamah died, her Yavam may marry her mother.

He holds that Ein Zikah (a Yevamah is not considered to be Mekudeshes to the Yavam. If he held that Yesh Zikah, her mother would be forbidden to him.)

Question: He should have said that the Halachah follows the opinion (Chachamim of R. Yehudah ben Beseira, 41a) that Ein Zikah!

Answer: Had he said so, one might have thought that this is only when there is more than one Yavam (since she can do Yibum with any brother, it is unreasonable to say that she is Mekudeshes to one), but when there is only one Yavam, Yesh Zikah!

Question: He should have said that the Halachah follows the opinion that Ein Zikah, even when there is one Yavam!

Answer: If so, one might have thought that this is true even when she is alive. Rather, he teaches that the Yavam may marry her mother only after she dies. When she is alive it is forbidden, for this uproots the Mitzvah of Yibum.

(Rav Yehudah): If a Yevamah died, her Yavam may not marry her mother.

He holds that Yesh Zikah.

Question: He should have said that the Halachah follows the opinion that says Yesh Zikah!

Answer: If so, one might have thought that is only when she is alive, but that Zikah ends after she dies. Therefore, he taught that Zikah does not vanish.

41a (Mishnah - R. Yehudah ben Beseira): If Reuven was Mekadesh his Yevamah's sister, he waits until his brother (Shimon) does Yibum or Chalitzah. After that, he may make Nisu'in. If the Yevamah died, he may make Nisu'in. If Shimon died, Reuven divorces his wife and does Chalitzah to the Yevamah.

(Shmuel): The Halachah follows R. Yehudah ben Beseirah.

18a (Abaye): Rav Yehudah learned (that Yesh Zikah) from Shmuel.

Question (Rav Yosef): Even if Rav Yehudah learned this from Rav (his other Rebbi), we could say that Amora'im disagree about Rav's opinion!

Answer (Abaye): Since Shmuel explicitly said that Yesh Zikah, it is better to say that Rav Yehudah received this from Shmuel, rather than to say that Amoraim argue about Rav's opinion.

(Rav Zvid): Rav Yehudah explicitly said in the name of Shmuel that after the Yevamah dies, the Yavam may not marry her mother.

This is consistent with Shmuel's ruling that the Halachah follows R. Yehudah ben Beseirah. It was necessary to say both of these:

Had he taught only that Yesh Zikah, one might have thought that this is only when there is only one brother. He ruled like R. Yehudah to teach that Yesh Zikah even when there are more brothers;

Had he taught only that the Halachah follows R. Yehudah, one might have thought that this is only while the Yevamah is alive, but after she dies the Zikah vanishes (and the Yavam may marry her mother). Therefore he taught that Zikah does not go away by itself.

41a - Question: (In the Mishnah, Reuven was Mekadesh Achos Zekukaso.) If she died, may he do Yibum?

Answer #1 (Rav): Yes.

Answer #2 (Shmuel): No.

(Rava): Rav holds that if a Yevamah was permitted, then forbidden, and the Isur lapsed, she becomes permitted again.

Rishonim

Rif and Rosh (2:1): Shmuel forbids the Yavam to his Yevamah's mother after the Yevamah dies, because Yesh Zikah. This is like Shmuel taught, that the Halachah follows R. Yehudah ben Beseirah (if Reuven was Mekadesh Leah, he waits until Shimon does Yibum or Chalitzah with Rachel).

Question: Kidushin of Achos Zekukaso should uproot Zikah!

Answer #1 (brought in Nimukei Yosef 3b DH Ad she'Ya'aseh): Zikah is like Kidushin. One Kidushin does not uproot another, but Nisu'in uproots Zikah.

Rejection (Nimukei Yosef): If Nisu'in uproots Zikah, also Kidushin mid'Oraisa should uproot Zikah, which is mid'Rabanan!

Answer #2 (Nimukei Yosef): Rather, Nisu'in does not uproot Zikah. This is why he must wait for his brother to do Yibum or Chalitzah, to remove Zikah.

Rif and Rosh: Shmuel needed to teach both of these, to teach that Yesh Zikah even when there are more brothers, and that even after the Yevamah dies, the Zikah does not vanish.

Rosh (2:1): Normally the Halachah follows Rav against Shmuel regarding Isurim. Here the Halachah follows Shmuel because the Gemara asked according to the opinion that Yesh Zikah, and the latter Amora'im explain Shmuel.

Rif (13b): If Reuven was Mekadesh Achos Zekukaso and she died, Rav permits Yibum and Shmuel forbids. The Halachah follows Rav. We normally follow Rav against Shmuel regarding Isurim. Also, if two sisters fell to Yibum and then one died, R. Yochanan (27b) agrees with Rav that if a Yevamah was permitted, forbidden, and then the Isur lapsed, she becomes permitted again. (They argue about if she was forbidden when she first fell.)

Rebuttal (Rosh 4:23): Perhaps R. Yochanan permits only when she was forbidden due to Zikah mid'Rabanan, but if she was forbidden mid'Oraisa, he agrees with Shmuel that she is permanently forbidden! Also Rav must distinguish similarly, for when two sisters fell to Yibum and one died, Rav (27b) permits even if the first one who fell died, even though the second was forbidden when she first fell.

Defense (of Rif - Korban Nesan'el 80): Rav distinguishes like this, but we have no source that R. Yochanan does!

Defense (of Rosh - Gra EH 159:26): The Yerushalmi (4:10) says that R. Yochanan holds like Rav.

Rosh (ibid.): Rather, we rule like Rav because the Halachah follows Rav against Shmuel in Isurim. Also, R. Chanina holds like Rav, and he is greater than Rav Asi, who supports Shmuel. Also, it is R. Elazar who forbids, and presumably Chachamim argue, just like they argue about one who remarried his divorcee.

Rambam (Hilchos Yibum 1:13): If one did Chalitzah with his Yevamah, just like she is forbidden to him, also her relatives are, such as her mother and daughter. She is forbidden also to his son and brother. Even her Shniyos are forbidden, e.g. the daughter of her daughter's daughter. She is likewise forbidden to the son of his son's son. The general rule is, it is as if he divorced her. Similarly, if she died amidst Zikah (before Yibum or Chalitzah), he is forbidden to her relatives as if she was married to him and died. All these Isurim are mid'Rabanan.

Rambam (7:8): If Reuven was Mekadesh Achos Yevimto, we tell him not to divorce her or make Nisu'in until his brother does Yibum or Chalitzah. If his brother did Yibum or Chalitzah or the Yevamah died, Reuven may make Nisu'in. If all his brothers died, he divorces his wife and does Chalitzah to the Yevamah. If his wife died before or after his brothers died, the Yevamah is permitted to him again.

R. Akiva Eiger (EH 159:7): The Ritva says that if his wife died after his brothers died, since the Yevamah was once dispelled from Yibum, she does not become permitted again. The Rashba permits her to marry the Yavam, but there is no Zikah and she may marry without Yibum or Chalitzah.

Rosh (ibid.): The Mishnah (41a) discusses when Reuven was only Mekadesh Achos Zekukaso. Then he must wait before making Nisu'in, lest it look like marrying Achos Zekukaso. If he already made Nisu'in he need not wait to have relations, for the Zikah went away entirely. This is only if he was Mekadesh her after her sister fell to Yibum. If not, she was never Achos Zekukaso, and Chachamim did not forbid.

Poskim

Shulchan Aruch (EH 159:5): If Rachel awaits Yibum with Reuven, Reuven is forbidden to her relatives. This is even if she died before Yibum or Chalitzah, whether or not there are other brothers.

Rema: Even if it is a Safek whether or not she is Zakuk to him, we are stringent.

Beis Shmu'el (11): This refers to a case like the Mordechai discusses, in which we do not know if Shimon died before or after his son. Reuven did Chalitzah due to the Safek, and now he wants to marry the Yevamah's sister. The Darchei Moshe says that perhaps we are stringent even if he did not do Chalitzah yet.

Shulchan Aruch (ibid.): Therefore, if Reuven was Mekadesh Rachel's sister Leah, he may not make Nisu'in, because she is like the sister of his Arusah. He waits for his brother Shimon to do Yibum or Chalitzah, which uproots the Zikah. Some say that if Reuven had Nisu'in with Leah, this uproots the Zikah, and he may have relations with her before Shimon does Yibum or Chalitzah.

Rema: Some say that nowadays that R. Gershom's Cherem forbids marrying two women, if a woman fell to Yibum the Yavam may not marry anyone else until doing Chalitzah. However, had he made Shiduchin with a woman before his brother died, he may marry her.

Source (Mordechai Kesuvos 291): The Cherem applies only to a woman he chose to marry. And even if it would apply to Yibum, there is a Cherem not to marry another woman after making Shiduchin (with Leah). Marrying Leah would override Yibum, for she came first. R. Yonah says that Achos Zekukaso is forbidden only if he was Mekadesh b'Isur after his brother died, but if he was Mekadesh first, the Isur of Achos Ishto overrides Zikah. The Charamos mid'Rabanan work similarly. If he was Meshadech first, the Cherem not to marry another after making Shiduchin overrides Zikah. And even according to the opinion that Kidushin does not uproot Zikah, we do not forbid his Arusah before his brother does Chalitzah or Yibum. R. Avigdor Kohen says that since the Halachah follows Aba Sha'ul, the Yevamah is destined to do Chalitzah, so the Cherem does not apply.

Gra (23,24): The Cherem applies because Zikah is like Kidushin.

Shulchan Aruch (6): If Reuven was Mekadesh Rachel and then his brother, who was married to her sister Leah, died, Reuven may make Nisu'in with Rachel.

Taz (11): This is only if Reuven has another brother. Sa'if 7 forbids in a case when he has no other brother.

Rebuttal (Hagahos Ma'aseh Nisim): Sa'if 7 discusses when Reuven was Mekadesh Rachel after her sister fell to Yibum. If he was Mekadesh her before Nefilah, we have no source to forbid when he has no other brother.

Shulchan Aruch (173:12): Reuven died, and his wife Leah fell to Shimon, then Levi was born, and Shimon died. Even if Shimon did not give a Ma'amar, his wife does Chalitzah, not Yibum. Since we hold that Yesh Zikah even without a Ma'amar, she is like Tzaras Eshes Achiv she'Lo Hayah b'Olamo.

Gra (18): Rav Ashi is Basra; he holds that Yesh Zikah, like R. Yochanan. Also Rava agrees.

Beis Shmu'el (15): Shiltei ha'Giborim (3b:3) says that we hold that mid'Rabanan, Yesh Zikah. R. Chananel (brought in Tosfos 27b DH Aval) holds that according to the opinion that Yesh Zikah, it is mid'Oraisa.