Gemara

(Rabah): The Torah obligates a borrower to swear (when he partially admits to the claim) because there is a Chazakah (of human nature) that a borrower is not brazen enough to (fully) deny the lender's claim;

If not for this, he would deny the entire claim.

Because borrowers are not brazen, he would like to admit to the full claim. He denied part of it to stall until he has the money to pay the loan. The Torah imposed the oath on him, in order that he will admit to the full claim. A Shomer is brazen enough to deny the claim, so he swears even for full denial.

Bava Metzia 3a (R. Chiya - Beraisa): If Reuven claimed 100 from Shimon, and Shimon totally denied it, and witnesses testify that he owes 50, he pays 50 and swears that he owes no more.

His own admission should not be stronger than witnesses (Modeh b'Miktzas must swear about the rest)!

5a: Every day people used to deposit animals with Levi (a shepherd), with witnesses. One day they gave to him without witnesses. He denied receiving the animals. Witnesses testified that he ate two of the animals.

R. Zeira: According to R. Chiya, Levi must swear about the rest.

Shevuos 40b (Rav Nachman): If Shimon totally denied a claim, he must swear a (mid'Rabanan) oath called Heses.

There is a Chazakah that one would not claim if he were not owed.

Objection: Just the contrary, Chazakah says that one is not so brazen to deny owing his creditor!

Answer: He intends to pay. He just wants to stall until he can pay.

(Rav Idi bar Avin): One who denies a loan is not disqualified from testifying. (We assume that he merely wants to stall.) One who denies a deposit is disqualified from testifying (surely he intends to steal it).

Bava Metzia 5b - Question (Rami bar Chama's Beraisa): The four Shomrim swear only when they partially deny and partially admit to the claim.

Why don't we say that since (he denies a deposit and) he is suspected to steal, he is suspected to swear falsely!

Answer: There, he is not suspected of stealing. He merely wants to stall until he finds the thief (if it was stolen) or finds the animal (if it was lost).

Question: If so, why is one who denies a deposit disqualified from testifying? Perhaps he is just stalling!

Answer: He is disqualified only when witnesses testify that when he denied it he knew that it was in his house, or he was holding it.

Rishonim

The Rif and Rosh (Bava Kama 9:28) bring Rabah's teaching.

Rosh: There is a Chazakah that one is not brazen enough to deny the claim of his creditor who knows that he is lying. Likewise, one cannot totally deny one who deposited with him. The Gemara mentioned a creditor, because loans entail only claim, admission and denial. Partial admission does not require brazeness. Therefore, there is no Migo (that he could totally deny the claim). Regarding a loan, the creditor knows that he is lying. One can brazenly lie about claims that apply only to deposits (since the depositer does not know what happened). Therefore, one is liable (to swear) even for full denial. If he were exempt, also Modeh b'Miktzas would be exempt due to a Migo, since he could totally deny without need to be brazen.

Hagahos Ashri (Bava Metzia 1:10 DH Af): Even if the deposit was in the Shomer's premises when he denied it, he is not disqualified. Perhaps he needed to use it temporarily. However, if he swore and then witnesses said that he was liable, he is disqualified.

Rambam (Hilchos To'en 1:1): If David claimed Metaltelim from Levi, and Levi admitted to part, he pays it, and swears about the rest mid'Oraisa.

Hagahos Maimoniyos (1): The Ri of Korvil asked, according to Ula who says that Shibud is mid'Oraisa, why does one swear Modeh b'Miktzas? We do not swear about debts with a lien on land! We must say that the borrower has no land, or the lender pardoned his lien.

Ran (Shevu'os Reish 24b): If David claimed from Levi 'you owe to me a loan of 50, and 50 for wounding me' (in a case in which we believe David to swear about the inhjury and collect), before David swore about the injury, if Levi denied everything, David swears and collects for the wound. Levi is exempt from Modeh b'Miktzas, because David did not have a claim of money, only a claim that leads to money. Perhaps David will not swear! After David swore, if Levi still denies everything, he must swear. This is like R. Chiya's law, in which Levi denies everything and two witnesses testify that he owes half. We are like witnesses that Levi really owes for the wounding, since David already swore.

Tosfos (107a DH Eruv): The Riva says that "Ki Hu Zeh" (which obligates one who partially admits to swear) refers to a loan. Also regarding a deposit, it applies only to claims that apply to loans (admission and denial). One can be brazen about a claim of Ones, therefore, he must swear even without admission. If one who did not admit were exempt, also one who partially admitted would be exempt, due to a Migo. However, one who denies (receiving the deposit) is exempt due to a Gezeras ha'Kasuv, even when he could be brazen.

Poskim

Shulchan Aruch (CM 87:1): If David claimed from Levi money or an object that Levi could have kept by claiming that he never received it, he returned it, or bought it from him, and Levi admitted to part, he must swear mid'Oraisa.

Rashba (2:206, cited in Beis Yosef 75 DH Kosav ha'Rashba): If David claimed 100, and Levi first said that he never borrowed, and later claims that he borrowed only 50 and paid it, he is established to be a Kafran (liar). He must pay the 50 (his initial denial is like admission that he did not pay it). We can investigate whether or not he must swear about the rest. It seems that he is exempt, for he never admitted that he owes.

SMA (1): The Shulchan Aruch excludes cases in which Levi could not keep the money. E.g. if David lent to Levi and said 'pay me back only in front of witnesses', or there are witnesses that he deposited an object with him, or Beis Din saw that Levi has the object, Levi could not make these claims. The same applies if David claims things that are normally lent or rented, and witnesses saw that Levi has it.

SMA (3): The Ir Shushan says that the reason for Modeh b'Miktzas is that the borrower wants to evade the lender until he will be able to pay. People are suspected about (trying to steal) money, but not to swear falsely. This is wrong. The Gemara concluded that people are as careful about theft as about false oaths. The Tur says so (92:5). Rather, the borrower intends to pay later. The Torah forces him to swear now. Surely, he will not swear (falsely). One who totally denies is exempt, for one who owes cannot totally deny. Chachamim enacted Shevu'as Heses, lest he has a Safek old debt against the lender (and totally denies, for perhaps he does not owe). He will not swear if he is unsure.

Gra (1): The Shulchan Aruch teaches that one swears not only regarding money. Rather, even regarding a deposit, perhaps he stalls, like it says in Bava Metzia (5b). Tosfos (5a DH l'Man) says that perhaps stalling applies even to land (he gave it for collateral, and plans to redeem it).

Gra (8): Rashi explains that one cannot be brazen to one who helped him (lent him). Tosfos disagrees, for if so one can be brazen to a depositor, and one who partially admits to a deposit should be exempt, since he could have totally denied! R.Tam explains that he lacks the audacity. The Riva says that this is only when the claimant knows that he is lying. The Gemara said that according to R. Chiya, Levi must swear about the rest. This shows that normally, one who denies a deposit is exempt.