Gemara

33a (Mishnah #1): If a vow forbids Levi to benefit from Moshe, Moshe may give the half-Shekel for Levi, or pay Levi's debt.

38a (Mishnah #2): If Reuven is Mudar Hana'ah from Shimon, Shimon may feed Reuven's wife and children, even though Reuven must feed them.

33b (Mishnah #3 - Chanan): If Reuven went overseas and Shimon fed Reuven's wife, he is not reimbursed;

The sons of Kohanim Gedolim say that he swears how much he spent, and he is reimbursed.

Kesuvos 108a - Question: Granted, he may give his half-Shekel, for this is a Mitzvah;

(Mishnah): When half-Shekalim are taken (from the chamber) for buying Korbanos, they have in mind people whose half-Shekalim were lost, collected, or will be collected.

But why may Moshe pay Levi's debt? This saves Levi money!

Answer #1 (R. Oshaya): Mishnah #1 is like Chanan, who says that if Shimon fed Reuven's wife, Shimon threw away his money.

Answer #2 (Rava): Mishnah #1 is even like Chachamim. The case is, the loan was on condition that the lender cannot demand payment.

Question: Granted, Rava did not explain like R. Oshaya, for Rava prefers to establish the Mishnah even like Chachamim. Why didn't R. Oshaya explain like Rava?

Version #1 - Answer: Granted, repaying such a loan is not like giving him money, but he spares him shame. (We follow the Bach's text.)

Version #2 - Answer: In Rava's case, he benefits him. He spares him shame.

Nedarim 33a: The Tana considers these benefits to be Mavri'ach Ari (mere prevention of damage). This is why they are permitted.

43a (Mishnah): Levi vowed not to benefit from Moshe, and Levi has nothing to eat. Moshe may tell a grocer 'Levi is Mudar Hana'ah from me. What will I do?'

The grocer supplies Levi, and Moshe pays for it.

Rishonim

Rif (Kesuvos 63b): Mishnah #1 is like Chanan, who says that if Moshe fed Levi's wife, Moshe threw away his money. In the Yerushalmi, Rabah bar Mamal says that Chanan and Bnei Kohanim Gedolim also argue about one who paid Levi's debt without his knowledge. R. Yosi says that Bnei Kohanim Gedolim say that if Moshe fed Levi's wife, Levi must compensate him, for Levi did not want her to starve. Regarding a debt, he can say 'I would have appeased David (the creditor), and he would have pardoned it.' This is even if David had a security.

Rambam (Hilchos Nedarim 6:4): If a vow or oath forbids Reuven to benefit from Moshe, Moshe may give the half-Shekel that Reuven is obligated to give and pay Reuven's debt. This is because nothing comes to Reuven; Moshe merely prevents the creditor from claiming from him. This is not included in Isur Hana'ah. Therefore, Moshe may feed Reuven's wife, children and slaves, even Kena'ani slaves, even though Reuven is obligated to feed them.

Beis Yosef (YD 221 DH Aval): According to the Rambam, the Mishnah (38a) that permits feeding his wife and children is like Chanan. The Gemara did not need to say so, for it already explained the Mishnah of paying a debt.

Rosh (Kesuvos 13:8): R. Oshaya answered that Mishnah #1 is like Chanan, who says that Moshe threw away his money. Since he cannot make Levi pay him, paying Levi's creditor is not considered giving Hana'ah. It is like mere Gerama (causation). If Levi may not benefit from Moshe, and Levi has nothing to eat. Moshe may tell a grocer, who will supply Levi, and Moshe pays for it. Even though Moshe causes Levi to get food, it is permitted because he does not give anything to him. It is mere Gerama. This is unlike doing Melachah for Levi. Even though he cannot make Levi pay for it, there he directly gave to him without anyone in between. R. Tam says that the only debt he may pay is feeding his wife, in which the debt was not clear. Even though one must feed his wife, if no one financed her, perhaps she would have economized and managed by herself. Even though the case is that Beis Din allotted to her food, she does not want people to consider her to be ravenous. Chanan agrees that one who paid a loan document did not waste his money. This is proper Hana'ah; Levi had no way to avoid paying. The Gemara suggested that the Mishnah is like Chanan, and it discusses feeding a wife. R. Chananel also explained like this. Rava answers that the Mishnah is even like Chachamim (the lender had pardoned the right to demand payment). The Riva proves from the Yerushalmi (cited above in the Rif) that Chanan and Chachamim argue about other debts. We learn from the Heter to give his Shekel, even though this is like a pressuring creditor with a security. R. Tam says that the Yerushalmi surely argues, for it says that Bnei Kohanim Gedolim agree that he may pay his debt, and R. Oshaya said that it is only like Chanan. The Yerushalmi says that he may pay his Shekel in any case, but the Bavli said that this is only if it was lost. Likewise, the Bavli holds that they argue only about feeding a wife, and the Yerushalmi disagrees.

Rosh (Nedarim 4:2): Rava establishes the case of paying his debt to be a loan on condition that the lender cannot demand payment. The borrower pays when he wants.

Rosh (Nedarim 4:4): Chachamim agree that Moshe may feed Levi's wife, for the Gemara did not say that the Mishnah (38a) is like Chanan. R. Tam says that he feeds her in front of Levi. Since he did not say anything, it is like a gift.

Poskim

Shulchan Aruch (YD 221:2): If a vow forbids Levi to benefit from Moshe, Moshe may pay Levi's debt. Even if the creditor had a security and Moshe took it, he returns it to Levi.

Beis Yosef (DH v'Da'as): Rashi, the Rif and Rambam hold like the Riva, that Chanan and Chachamim argue about all debts.

Shach (6): He may not pay with Levi's knowledge. The Bach rules like those who permit only a Milveh Al Peh, but not when there is a document. However, if the borrower need not pay until he wants, Moshe may pay with Levi's knowledge, even if there is a document or security. However, he may not return the security.

Question: The Rosh in Nedarim (4:2) says that Rava establishes the Mishnah to discuss a loan on condition that the lender cannot demand payment. This implies that one may not pay a standard loan! Why did the Rosh omit R. Oshaya's answer, that our Mishnah is like Chanan?

Answer #1 (Beis Yosef DH l'Kach): Even though Chanan exempts the borrower regarding any loan, Rava holds that Chanan forbids paying other loans for a Mudar Hana'ah. The Halachah follows Rava, for he is Basra.

Question: The Gemara said that Rava did not answer like R. Oshaya, for Rava prefers to establish the Mishnah even like Chachamim. It should have said that Rava holds that Chanan agrees that it is forbidden for a Mudar Hana'ah!

Answer (Beis Yosef DH v'Ein): The Gemara gave a better answer. Even if Rava would hold like R. Oshaya, who holds that Chanan permits for a Mudar Hana'ah, it is better to establish the Mishnah like everyone. Alternatively, the reason Rava disagrees with R. Oshaya (who says that Chanan permits for a Mudar Hana'ah) is because it is better to establish the Mishnah like everyone.