Gemara

(Reish Lakish): Since Kofer is not paid in her lifetime, only after death, it is only Ra'uy (apt to come). A husband inherits only what was Muchzak (in her possession), not what was Ra'uy.

Rishonim

Rambam (Hilchos Nachalos 1:11): If Levi's wife died, and afterwards Morishah (a relative who was destined to bequeath to her).died, Levi does not inherit her. A husband inherits only what came to her Reshus before she died, but not Ra'uy.

Magid Mishneh: The Rambam did not teach whether or not a husband inherits a loan owed to his wife. He taught (3:1,5) that a Bechor does not get a double portion of a loan, for it is Ra'uy. However, in Hilchos Ishus (22:7) the Rambam says that a husband inherits all property of his wife, i.e. Nichsei Melug (i.e. property that she brought into the marriage, and it is returned to her as is if she is widowed or divorced) ... He does not distinguish at all between different kinds of property. It seems that he holds like his Rebbi, the Ri mi'Gash, who says that a husband inherits a loan. Regarding a loan without a document, he distinguishes between whether or not payment was due before she died. The Ri mi'Gash did not act according to his opinion, out of concern for the Rif and R. Chananel, who equate a husband to a Bechor. The Ramban and Rashba hold like the Ge'onim, that a husband does not inherit a loan. This is primary. This is only if it is clear that the loan was from her. If she does business in the house, and there are documents in her name, there is no Chazakah that they belong to her (so he collects them).

Rosh (Bava Basra 8:11): He does not inherit her loan. Tosfos says that this is even if she lent her Nichsei Melug while married and she died before collecting it, her husband inherits it. We learn from Bava Kama 42b. One does not inherit damages owed to his wife according to Rabanan, for it is like a loan, even though had it come to her in her lifetime it would have been Nichsei Melug.

Rebuttal (Rosh): I say that if she lent her Nichsei Melug while married, her husband inherits it, for she had no right to lend the principal. The principal is in her husband's Reshus to eat the Peros. Her loan is no better than her sale. In Usha they enacted that her husband takes from the buyer; it is as if he is the first buyer. All the more so, if she lent money in her possession, her husband takes from the borrower and inherits the loan.

Bach (EH 90 DH u'Mah she'Chosav ba'Meh): Perhaps Tosfos discusses money from which, before Nisu'in, her husband waived his rights to it in her lifetime; she consumes the Peros and revenue from it. This is why It is called her Nichsei Melug. Alternatively, it is property from which a husband does not eat the Peros (EH 85). Tosfos did not say her Nichsei Melug, but the Rosh and Mordechai say so in the name of Tosfos. I say that Tosfos' opinion is primary. Perhaps the Rosh would agree; he argued because he thought that the Ri discusses regular Nichsei Melug. Perhaps this is why the Shulchan Aruch discussed a loan of Nichsei Melug, without saying 'her'.

Poskim

Shulchan Aruch (EH 90:1): If others owed a loan to a woman when she married, and she died before collecting it, her husband does not inherit it.

Rashba (Teshuvah 63 attributed to Ramban, cited in Beis Yosef DH Kosav ha'Rashba): Rav Papa taught that a Bechor does not inherit a double portion of a loan, and a husband does not inherit Ra'uy. He did not teach them together. Some, including the Ri mi'Gash, infer that this is because a husband inherits a Ra'uy loan. Most hold like the Rif and R. Chananel, who say that also a husband does not inherit a loan. Presumably, this applies only to a loan that she inherited, or she lent before Nisu'in, or lent from money she saved for herself, i.e. her husband waived his rights to it during Eirusin, or after Nisu'in with a Kinyan. If not, he has rights to the money like Nichsei Melug, and she cannot divert the money from him. Her stipulation before Nisu'in cannot help without his consent. If not, there would be no need for a Shtar Mavrachas (before Nisu'in she writes her property to a relative, so her husband will not get it). When the Gemara discusses a married woman with her own money, it says that her husband stipulated during Eirusin, or someone gave to her on condition that her husband will have no rights to it. It did not mention that she left money for herself, which is much more common, for it does not help. All the more so if she lent to her husband after Nisu'in, he acquires it like Nichsei Melug. Even if he waived his rights (in her money), he inherits half the loan, just like a Bechor who lent to his father collects an extra half-share of it, for it is a Safek whether Bechorah applies to it (Bava Basra 126a). If she had Mashkanta (land for collateral for a loan), in a place where the borrower cannot redeem his land before the set time, her husband inherits it, for it is as if she acquired it. Even a Bechor gets an extra share of it (Bava Metzia 67b). A Stam Mashkanta is like a place where the borrower cannot redeem it. A place where he can redeem it is only if he can do so even the same day.

Chelkas Mechokek (8): The Mordechai says that if she had a security for a loan, all agree that a Bechor gets a double portion, for a creditor acquires a security. The same applies here. A husband inherits such a debt, for it is as if was collected, even if the security was taken at the time of the loan. If one had a loan from his wife and she died, he is Muchzak in it and inherits it. If a Bechor borrowed from his father, it is a Safek, for it says "b'Chol Asher Yimatzei Lo)", i.e. what the father had. Here, it is not Ra'uy, for her husband has the money. However, the Rashba says that he inherits only half.

Beis Shmuel (9): Any loan considered Muchzak regarding a Bechor is Muchzak regarding a husband.

Shulchan Aruch (ibid.): However, if she lent her Nichsei Melug and she died before collecting it, her husband inherits it.

Chelkas Mechokek (9): The Rosh says that this is because she was not permitted to lend them. It seems that if her husband had no rights to eat the Peros, she may lend them, so it is Ra'uy, like money she lent before Nisu'in. However, we can distinguish. When he marries her, he becomes like a buyer. Even though he does not eat the Peros, he inherits her, and she cannot make it Ra'uy to uproot his inheritance against his will. Whatever she cannot sell, she cannot lend it to make it Ra'uy. The Rashba says that she can do so only if he wrote that he has no Reshus in it.

Beis Shmuel (11): The Rosh and Terumas ha'Deshen connotes that he can take the Nichsei Melug from the borrower even in her lifetime, for he has rights to eat the Peros. If he did not do so and she did not collect, he inherits. Even the Rambam, who does not allow him to take the property itself, would not consider this Ra'uy. The Rambam holds that a husband inherits even a loan! Also, perhaps the Rambam holds that he can take a loan. It is unlike property, for one cannot make a buyer lose his land.

Rema: Any property she had from which he does not eat the Peros, if she lent it to others, he does not inherit them.

Beis Shmuel (12): If she wrote a Mavrachas document, the sale is valid and the buyer eats the Peros. If she sold Tovas Hana'ah of her Kesuvah, she may give (or lend) the money to whom she wants. In both cases, he does not inherit. The third case in which he does not eat the Peros is if he gave a gift to her after Nisu'in. However, he eats the Peros of the Peros, so he inherits it.