Gemara

Chachamim learn that only an Eved Ivri sold by Beis Din receives Ha'anakah (gifts when he leaves) from "you will give to him", not to one who sold himself.

R. Elazar learns from the verse that we do not give the gifts to his creditor. Normally, R. Noson's law applies. This is an exception.

Beraisa (R. Noson): "He will give to the one he sinned against" - if Reuven owes Shimon, and Shimon owes Levi, we take from Reuven to pay Levi.

Chachamim disagree with R. Noson (so no verse is needed to teach that his law doesn't apply here).

Pesachim 31a (Rava): If lender sold or was Makdish property before he collected it for his debt, this is invalid. The collection is not retroactive, since the borrower could have paid money and kept his property.

Question: Rava cited Rav Nachman to say that if orphans collected land for their father's debt, their father's creditor can collect from it. If a lender does not collect retroactively, this is like orphans who bought property after their father died!

Answer: The creditor had a lien on what they collected, due to R. Noson's law.

Rishonim

Rif and Rosh (Kesuvos 6a and 2:9): If Reuven owes Shimon, and Shimon owes Levi, we take from Reuven to pay Levi.

Tosfos (Kidushin 15a DH v'Idach): The Halachah does not follow R. Eliezer, for he was from Beis Shamai. The Halachah follows the first Tana. Also, R. Simlai said that he would have counseled a Mamzer how to have Kosher children: steal, be sold to be an Eved Ivri, have children from a Shifchah, and free them. According to R. Eliezer, he could sell himself without stealing, and still be permitted to a Shifchah! R. Tam and the Ri rule like R. Noson, for Rava rules like him, according to Rav Nachman. We following Rav Nachman in monetary laws. Even though we rule like Chachamim regarding a Shifchah, we rule like R. Eliezer in other respects. Alternatively, R. Simlai showed how he could permit his children according to all opinions. Most texts say that R. Elazar argues with Chachamim. R. Nesan'el says that regarding a loan, all hold like R. Noson. The Gemara said that R. Elazar learns from the verse that the slave's creditor does not get the Ha'anakah. Normally, R. Noson's law applies to wages. Chachamim hold that R. Noson's law never applies to wages, for he toiled bodily for them.

Rambam (Hilchos Malveh 2:6): If Reuven owes 100 to Shimon, and Levi owes 100 to Reuven, we take from Levi and give to Shimon.

Question (Lechem Mishneh): The Rambam rules like R. Noson (like R. Eliezer), and also that one who sells himself does not receive Ha'anakah (like Chachamim)! It seems that the Rambam holds like R. Nesan'el. If so, here he refers only to loans, but not to Sechirus (rental or wages), even though he did not specify. Perhaps it sufficed that he taught that a creditor does not collect Ha'anakah, for also this is called Sechirus.

Rebuttal (Shach CM 86:3): If so, the Rambam should have explicitly said that Shibud d'R. Noson does not apply to Sechirus. The Rashba (Gitin 37a DH Lo) says that perhaps Chachamim agree to R. Noson's law. He excludes one who sells himself, for It is more reasonable that a verse about a slave excludes matters of slaves than matters of creditors. The Gemara said that he argues with R. Noson's law, for it preferred to say that they argue about the Halachah, and not just how we expound. However, we can rule like R. Noson and also like the first Tana. The Ritva (Kidushin 15a DH Lo) says that Rav Tivyumi was forced to say that the first Tana argues with R. Noson, for he holds that Chachamim also learn the Gezeirah Shavah "Sachir-Sachir" (14b). The Stam Gemara disagrees; Chachamim can expound "Lo" like R. Eliezer. Alternatively, the Rambam holds almost like R. Nesan'el. Ha'anakah is due to Tzedakah; R. Noson's law does not apply to such matters, e.g. Ma'aser Oni. A Tosefta teaches that one may not pay a debt with Ma'aser Oni. The Rambam (Hilchos Matanos Aniyim 6:17) and Avi ha'Ezri (in Mordechai Bava Basra 497) say that one who owes money need not pay from Tzedakah that he received. Therefore, the Gemara said that in general (matters of Tzedakah), Chachamim holds that R. Noson's law does not apply.

Gra (6): We can explain R. Nesan'el like the Ritva.

Hagahos Ashri (Bava Kama 4:4, citing Or Zaru'a): R. Noson's law applies to debts due to loans, damage, Sechirus, theft, and Shomrim.

Hagahos ha'Gra: The other Poskim disagree. See Kidushin 15a (Shibud d'R. Noson applies to Ha'anakah, i.e. even though the slave's debt preceded his master's obligation)! Hagahos Ashri must hold that the first Tana holds that Shibud d'R. Noson does not apply in such cases, and rules like him.

Note: Perhaps he could hold that the Shibud on the master begins when he bought the slave, even though he does not pay until the slave leaves. Some say that Shibud d'R. Noson applies to a Kesuvah while she is married.

Poskim

Shulchan Aruch (CM 86:1): If Shimon owes 100 to Reuven, and Levi owes 100 to Shimon, we take from Levi and give to Reuven.

Beis Yosef (DH Reuven): Tosfos says that we rule like R. Noson because Rava (Pesachim 31a) must hold like him. The Rashba (961) has a tradition that the Halachah follows R. Noson, and there are many proofs for this.

Shulchan Aruch (ibid.): We do not distinguish whether there are documents for the loans or they are Milvos Al Peh.

Gra (3): When Shimon has other property, Reuven may not collect from Levi (Sa'if 2), for this is like Meshubadim when there are Bnei Chorin. We do not call Levi's property Meshubadim to say that a Milveh Al Peh cannot collect from it. The Yerushalmi says that the Mishnah (Kesuvos 84a) discusses a Milveh Al Peh collecting from money owed to a man. We hold that a debt written in the Torah is like a Milveh Al Peh; Shibud d'R. Noson applies even when both debts are like this (Bava Kama 40b).

Shulchan Aruch (ibid.): Since the borrowers admit, we take from Levi and give to Shimon. It does not matter if Levi owes for a loan, purchase or Sechirus.

Beis Yosef (DH u'Mah she'Chosav b'Chol): Sefer ha'Terumos says that some say that Shibud d'R. Noson applies only to loans and debts due to purchases, but not to Sechirus or Ha'anakah, for we hold like R. Eliezer, who expounds to exclude Ha'anakah. Sefer ha'Terumos agrees that the verse excludes Ha'anakah, but we have no source to exclude Sechirus.

Bach (Sof Siman DH Kosav): The text of Sefer ha'Terumos should say (the first opinion rules like) the first Tana of R. Eliezer', like R. Nesan'el in Tosfos (the first Tana holds that Shibud d'R. Noson does not apply to any Sechirus).

Rebuttal (Shach 3): According to the Bach's text, we cannot explain Sefer ha'Terumos (there is a source to exclude Sechirus)! The Beis Yosef's text is correct (he does not hold like R. Nesan'el. Chachamim never hold like R. Noson, and R. Eliezer holds like him everywhere except for Ha'anakah.)

SMA (2): The Tur and Shulchan Aruch did not mention that it does not apply to Ha'anakah, for this does not apply nowadays. Alternatively, the Tur and Shulchan Aruch discuss debts. Ha'anakah is a gift, not a debt.

Shach (2): The Maharshal says that Shibud d'R. Noson applies to all debts, even if Levi's debt is for a different reason than Shimon's.

Gra (5): Pesachim 31b shows that it applies to money owed for a purchase.