Gemara

(Beraisa): "Sheiro (his close relative)" refers to his wife. The verse teaches that a husband inherits his wife.

159b (Abaye): The Torah mentions Sivah (transferal of inheritance to another tribe) regarding a son and a husband (who inherit their mother and wife, respectively). Just like a husband in the grave does not inherit, also a son.

Kidushin 45b: A man agreed to his daughter's Kidushin (to a Kohen), and went abroad. She had Nisu'in.

(Rav): She may eat Terumah until the father returns and protests.

(Rav Asi): She may not eat, lest he return and protest!

(Rav Shmuel bar Rav Yitzchak): Rav admits that if she dies before the father returns, her husband does not inherit her. We leave the money in its Chazakah (her father inherits her, perhaps the Nisu'in was invalid).

Gitin 73b (Beraisa - R. Yehudah): (If a man gave a Get to take effect at the last moment he is in the world,) in the interim, he receives her earnings; he can annul her vows; (if she would die) he inherits her... She is like his wife in every respect, just she does not need another Get.

R. Meir says, her Bi'ah with another man is contingent;

R. Yosi says, if she has Bi'ah with another man, it is a Safek;

Chachamim say, she has the stringencies of being divorced and not divorced, provided that he (eventually) dies from the sickness.

Chachamim and R. Yosi argue about whether he must feed her.

Rishonim

Rif and Rosh (Kesuvos 27a and 5:35): Only proper divorce uproots inheritance mid'Oraisa.

Rambam (Hilchos Nachalos 1:8): A man inherits his wife mi'Divrei Sofrim.

Rebuttal (Ra'avad): There are many proofs against this, including the end of Perek 9 of Bava Basra.

Magid Mishneh: There is an argument about this in the Gemara. The Rambam rules like Rav (Kesuvos 83b). Perhaps this is because we hold that one can stipulate not to inherit an inheritance that comes from elsewhere, i.e. a wife, which is only mid'Rabanan. However, others explain 'it comes from elsewhere', i.e. due to his action (marriage), unlike inheritance of blood relatives, which is automatic. The Rambam himself explains this way in Hilchos Ishus 23:6,7)! The Ra'avad learns from Bava Basra 159b. The Rashba brought other proofs that it is mid'Oraisa.

Kesef Mishneh: One could have said that the Rambam holds that it is mid'Oraisa, but he calls it mi'Divrei Sofrim because it is not explicit in the Torah. However, in Halachah 6:8 he says that Chachamim strengthened a husband's inheritance like Torah law, even though it is mid'Rabanan.

Rambam (9): If one was Safek divorced, her husband does not inherit her.

Rebuttal (Ra'avad): If a man lodged with his ex-wife in an inn, Beis Hillel require another Get. The Yerushalmi says that this is for inheritance. I.e. even though he Vadai divorced her and we are unsure if he remarried her, he inherits her. If he Safek divorced her, all the more so he inherits her!

Magid Mishneh: I did not find a total proof for the Rambam. Perhaps he learns from a man who agreed to his daughter's Kidushin to a Kohen, and she had Nisu'in when he was abroad, Rav permits her to eat Terumah. However, Rav admits that he does not inherit her, for we leave the money in its Chazakah. The Ba'al ha'Itur says that he does not inherit her in any case of Safek Kidushin or Safek divorce. The Rambam agrees. However, one could distinguish. Before Nisu'in, her father was Muchzak to inherit her. Before divorce, her husband was Muchzak to inherit her. Perhaps we do not change this Chazakah due to a Safek! Gitin 73b supports the Rambam. Tana'im argue about a Safek divorcee. R. Yehudah (who considers her to be Vadai married) says that he inherits her, but the other Tana'im do not mention this. Also, if a husband inherits even a Safek divorcee, R. Yehudah would not need to teach that he inherits her! The Yerushalmi actually supports the Rambam! R. Elazar says that after he was secluded with his ex-wife, he inherits her, like we learned that a husband receives her earnings, and he can annul her vows... Ze'ira derives that she is like his wife in every respect. If one inherits a Safek divorcee, Ze'ira could not infer this! However, perhaps he derived this from the fact that he can annul her vows. This is mid'Oraisa, so we would be stringent if it were a Safek. In any case the Yerushalmi does not refute the Rambam, for it holds that she is Vadai married. If it were Safek Kidushin, how could we take the inheritance from her father due to a Safek? Later, I found that Ge'onim argue about this.

Lechem Mishneh: How can the Magid Mishneh bring a proof from the Yerushalmi for the Rambam, which discusses Safek Kidushin? Perhaps divorce is different, for he is Muchzak! The Magid Mishneh means that according to the Ra'avad, who does not distinguish Kidushin from divorce, the Yerushalmi supports the Rambam. Why didn't R. Elazar say that after seclusion, he can annul her vows? This is a bigger Chidush, because (there is a gap in the text). He must hold that inheritance is a bigger Chidush, for one would think that we leave money in its Chazakah. We find that we do not follow the majority regarding money, but we do for capital cases.

Lechem Mishneh (edition #2): The Yerushalmi holds that her husband inherits when there is Safek Kidushin. The Bavli (Kidushin 45b) disagrees. The Ra'avad holds that there is no source to say that they argue about Safek divorce.

Hagahos Chever ben Chayim (in Likutim in Frankel Rambam): The Rambam holds that a husband inherits mid'Rabanan. We are lenient about a Safek Isur mid'Rabanan, and all the more so regarding Safek Mamon. We cannot challenge the Rambam from the Yerushalmi, which holds that a husband inherits mid'Oraisa.

Rosh (Bava Basra 9:16): The Rashbam holds that that if a man intended to divorce his wife, he does not inherit her. There is no proof for this.

Poskim

Shulchan Aruch (EH 90:5): If a woman was Safek divorced and died, her husband does not inherit her.

Chelkas Mechokek (14): The Tur says that only full divorce uproots inheritance. It seems that Safek divorce has the same the law as when we are unsure who died first (Sa'if 6; his heirs inherit the Ikar Kesuvah and addition, her heirs inherit the Nichsei Melug, and they divide the Nichsei Tzon Barzel).

Beis Shmuel (20): The Rambam equates this to the law of an Arusah who had Nisu'in in her father's absence. Her husband does not inherit her, for it is a Safek; perhaps her father did not approve. The same applies to a Safek divorcee. The Magid Mishneh rejected the proof, and the Ra'avad disagreed with the law. The Magid Mishneh concluded that Ge'onim argue about this. Therefore, if her husband seized the inheritance, he keeps it.

Be'er ha'Golah (40): The Rashbam holds that once one intends to divorce his wife, he does not inherit her. The Rosh holds that only proper divorce uproots his inheritance. I think that the Shulchan Aruch means that he does not inherit the property Muchzak to her, but we do not take from him what is Muchzak to him, for a Safek cannot take from a Vadai. This is like a house that fell on both of them in the next Sa'if.

Mekor Baruch (7 6:4, in Likutim in Frankel Rambam): We should say that the husband is Vadai, and her family is Safek, and they cannot take from him! Also, this should be no worse than when a house fell on him and his wife and we are unsure who died first. The Rambam rules that they divide the Nichsei Tzon Barzel. Also, an heir is no better than the one whom he inherits. If she were alive, she could not collect her Kesuvah! Even a woman who may remarry based on one witness that her husband died collects only Ikar Kesuvah, because we expound the Kesuvah (when you will be permitted to remarry...), but not additions or Nichsei Tzon Barzel. The Nimukei Yosef says so in the name of the Ritva (Yevamos 117a DH she'Chen) and also the Magid Mishneh (Hilchos Ishus 16:26) says so. All the more so a Safek divorcee cannot collect. If she remarried, we would force her to leave! Why do her heirs inherit her Kesuvah?!

Sha'ar ha'Melech (Hilchos Ishus 10, Chupas Chasanim 4): A house that fell on both of them is different, for there both lost their Chazakos. Here, the husband is still Muchzak.