Gemara

81b (Mishnah): If Reuven lent to Shimon (relying) on a security, he is a Shomer Sachar on it.

Our Mishnah is unlike R. Eliezer:

(Beraisa - R. Eliezer): If Reuven lent to Shimon (relying) on a security and lost the security, he swears (that he lost it) and collects the debt.

R. Akiva says, he lent only due to the security. If he lost it, he lost the loan.

82a - Suggestion: They argue about Shmuel's law, when the security is worth less than the loan.

(Shmuel): Reuven lent 1000 Zuz and took an axe handle like a security; if he loses the handle, he loses the whole loan. (R. Akiva holds like Shmuel; R. Eliezer argues, the security was only taken like a reminder of the loan.)

Rejection: All disagree with Shmuel. In such a case, all agree that he can still collect. The Tana'im discuss a security taken at the time of the loan. They argue about whether a Shomer Aveidah is a Shomer Chinam or a Shomer Sachar.

Suggestion: Rav Yosef's law is like R. Akiva, and R. Eliezer disagrees.

Rejection: No, all can agree with Rav Yosef. They argue about when the lender needs the security. R. Akiva says that we still consider the loan to be a Mitzvah, therefore he is a Shomer Sachar (for Rav Yosef's reason);

Nedarim 33b - Version #1 (R. Ami or R. Asi): If Shimon is Mudar Hana'ah from Reuven, he may not return an Aveidah to Reuven, for Shimon would save Perutah d'Rav Yosef due to Reuven:

Bava Kama 56b (Rabah): A Shomer (one who guards an) Aveidah is considered a Shomer Chinam (he is exempt if it stolen or if he loses it);

(Rav Yosef): He is considered a Shomer Sachar (and is liable for loss or theft).

Rabah says he is considered a Shomer Chinam, for he gets no benefit.

Version #1: Rav Yosef considers him to be a Shomer Sachar because it is a Mitzvah to guard an Aveidah, and this Mitzvah exempts him from giving bread to a poor person (who requests).

Version #2: Rav Yosef says that since the Torah obligated him to guard the Aveidah, he is like a Shomer Sachar. (end of Version #2)

Nedarim 33b (The other of R. Ami and R. Asi): Shimon may return to Reuven. It is rare that one saves money through Rav Yosef's law.

34a - Version #2: All agree that the Mudar may return Shimon's Aveidah. It is rare that one saves money through Rav Yosef's law, so we are not concerned for this;

Gitin 74b: (If a Get was given 'on condition that you return my garment', and it was lost, R. Shimon ben Gamliel and Chachamim argue about whether or not it suffices for her to return its value. If a sharecropper was asked to irrigate more than normal for extra wages, and rain came, eliminating the need for extra irrigation, Rabah and Rav Yosef argue about whether or not he gets the extra wage promised.)

Suggestion: Rav Yosef holds like Chachamim, and Rabah holds like R. Shimon ben Gamliel.

Rejection: This cannot be! We hold that the Halachah follows Rabah, and here (in our Mishnah) we hold that the Halachah does not follow R. Shimon ben Gamliel!

Rishonim

Rif (Bava Kama 24a): The Halachah follows Rav Yosef, for the Gemara in Bava Metzia (82a) and Shevuos (44b) say that all hold like him.

Rambam (Hilchos Gezeilah 13:10): As long as the Aveidah is with the finder, if it was stolen or lost he is liable. If Ones occurred, he is exempt. A Shomer Aveidah is like a Shomer Sachar. Since he is engaged in a Mitzvah, he is exempt from several Mitzvos Aseh as long as he is engaged in guarding the Aveidah.

Rosh (Bava Kama 6:4): Rav Yosef says that a Shomer Aveidah is like a Shomer Sachar because if an Oni will come while he is caring for the Aveidah, he is exempt from giving bread to him. Rabah holds that this does not suffice to make him a Shomer Sachar, for it is rare that an Oni comes while he is caring for the Aveidah.

Rosh (Bava Metzia 2:17): BaHaG and R. Chananel rule like Rav Yosef, because in Nedarim it says that all agree that a Shomer Aveidah is exempt from Tzedakah. They only argue about whether or not it is common enough to forbid a Mudar Hana'ah. The Ri disagrees. Rabah agrees that Osek b'Mitzvah Patur Min ha'Mitzvah. He just says that this does not make him a Shomer Sachar. The Halachah follows Rabah against Rav Yosef with only three exceptions. Some say that this refers only to Bava Basra; it seems that it applies to all of Shas. The Gemara (Gitin 74b) said 'the Halachah follows Rabah, and here (in our Mishnah) the Halachah does not follow R. Shimon ben Gamliel! Had the Gemara meant 'here we hold that the Halachah follows Rabah', it would have said so, just like it said 'here the Halachah does not follow R. Shimon ben Gamliel!' There are proofs for both opinions.

Poskim

Shulchan Aruch (CM 267:16): As long as the Aveidah is with the finder, if it was stolen or lost he is liable, like a Shomer Sachar.

Beis Yosef (DH u'Mah she'Chosav b'Shem): In a Teshuvah, the Rosh rules like Rav Yosef. The Tur says that he retracted in his Pesakim, and rules like Rabah. This is not clear; he brings both opinions in his Pesakim. In any case, we follow the majority of Poskim, who rule like Rav Yosef.

Rema: Some say that he is like a Shomer Chinam. The law is the same as we wrote regarding a security (72:2).

SMA (17): Regarding a security the Rema rules that some say that he is like a Shomer Chinam. Due to the Safek we do not make him pay.

Yam Shel Shlomo (Bava Kama 6:9): The conclusion is like the latter version, in which Rav Yosef agree that the exemption from Tzedakah does not make one a Shomer Sachar. (Rather, it is because the Torah obligated him to guard the Aveidah.) We must say that the exemption from Tzedakah suffices to forbid a Mudar Hana'ah to return an Aveidah (according to the opinion that forbids), but it is not enough to make one a Shomer Sachar.

Or Some'ach (Hilchos Sechirus 10:1 DH v'Hinei): Everywhere, the Gemara holds like Version #1. Perhaps Version #2 was an addition of the Ge'onim. I would explain that it distinguishes between a Shomer Aveidah and a Shomer Chinam. The Magid Mishneh (Hilchos She'alah 7:11) anything a Shomer Aveidah can retract in the middle and force the owner to take back his deposit, but a Shomer Chinam cannot. This is because a Shomer Chinam merely needs to leave the deposit in a guarded place. Regarding a Shomer Aveidah it says "Hashev Teshivenu". If he found an animal that does not work, he must sell it. He must shake out a garment... He is obligated to care for it like a slave, therefore he can retract, because we are Avadim only to Hash-m! Surely, this shows that he is like a Shomer Sachar!

Question: Perhaps we follow the first version, in which Rav Yosef holds that the exemption from Tzedakah makes him a Shomer Sachar!

Answer (Yam Shel Shlomo): If so, all the more so he holds that a Mudar Hana'ah may not return an Aveidah. If so, surely the Halachah does not follow Rav Yosef, for we permit a Mudar Hana'ah to return an Aveidah! All the Ge'onim say so. We permit to cover the blood (of a slaughtered bird or Chayah) with dirt of an Ir ha'Nidachas. Even though it is Asur b'Hana'ah, fulfilling Mitzvos is not considered Hana'ah. A Shofar or Lulav of an Ir ha'Nidachas would have been Kosher if no Shi'ur were required. We do not say that he benefits from Isurei Hana'ah by being exempt from Tzedakah at the time he uses until for a Mitzvah! The Halachah follows Rabah.

Rebuttal (Shach 14): The Rosh (it seems that it should say 'Ran') in Nedarim 33b DH Perutah says that a Mudar Hana'ah may return an Aveidah because Perutah d'Rav Yosef is rare. Nevertheless, it suffices to make him a Shomer Sachar. Tosfos (Shevuos 44b DH v'Rav) asked about saving Perutah d'Rav Yosef while using Isurei Hana'ah for Mitzvos. He answered that Perutah d'Rav Yosef applies to an Aveidah or security because one must regularly spread it out (lest it get moldy), and an Oni might come at such a time. One can arrange to blow a Shofar (or immerse in a Mikveh) of Isurei Hana'ah at a time when no Oni will come. (In this way, he avoids getting Hana'ah.)

Conclusion (Shach): The Rema (72:2), SMA and all the Acharonim say that it is a Safek if the Halachah follows Rabah or Rav Yosef. If the one who lost the Aveidah seized the money from the finder, we do not force him to return it.

Shulchan Aruch (72:2): If one lent on a security, he is a Shomer Sachar.

Rema: Some say that he is only a Shomer Chinam. Since it is a Safek, we do not force one to pay.