Sumchus holds that when there is a Safek regarding money it is split between them
If two people are holding a Talis and each one claims that the entire Talis belongs to him the Chachamim decreed that each one shall take a Shevu'ah in order to deter a person from grabbing his friend's Talis and claiming it is his.
If two people deposit money with a Shomer, one deposits 100 and the other deposits 200 and each one claims that he deposited 200 the Rabanan hold that each one receives 100 and the rest is put away until the arrival of Eliyahu ha'Navi. (1)
R. Yosi says that all of the money is put away until the arrival of Eliyahu ha'Navi because otherwise the one who is lying has nothing to lose.
If a Ba'al ha'Bayis instructs a storekeeper to provide goods to his workers on credit and the workers claim they didn't receive it and the storekeeper claims that he provided it both the workers and the storekeeper swear and collect from the Ba'al ha'Bayis.
R. Chiya says that if someone claims that his friend owes him 100 and the friend denies it and witnesses testify that he owes 50 he must swear a Shevu'as Modeh b'Miktzas. (2)
Rabah says that the reason why the Torah obligates a person who is Modeh b'Miktzas to swear is because a person doesn't have the Chutzpa to deny a loan entirely and therefore he denies it only partially. (3)
If a person admits that he owes money it is tantamount to the testimony of 100 witnesses, however if a person admits a Knas he is Patur.
If a person admits that he owes money he is Chayav to pay even if two witness testify that he is not Chayav
A person is Chayav a Korban if he admits that he did an Aveirah which is Mechayev him a Korban.
If two witnesses testify that someone ate Chelev and he denies it R. Meir holds he is a Chayav a Korban while the Chachamim disagree.
If two witnesses testify that someone is Chayav a Chomesh and he denies it R. Meir holds he is a Chayav a Chomesh while the Chachamim disagree. (4)
One witness is not Mechayev a person money but he is Mechayev him a Shevu'ah.
A BIT MORE
1. Since one of them is certainly lying and the money belongs to only one of them the money is put away, however in the case of two people holding in to a Talis it is possible that they picked it up at the same time and it belongs to both of them and therefore the money is split with a Shevu'ah..
2. It is a Kal va'Chomer if a person is Chayav a Shevu'as Modeh b'Miktzas upon his own admission he is certainly Chayav a Shevu'ah upon the testimony of witnesses.
3. Even though he partially denies the loan he is not suspected that he will swear falsely because he would have liked to admit the loan completely but he admitted it only partially in order to buy some time therefore the Torah obligates him to swear so that he will admit it entirely.
4. A person is Chayav a Chomesh for eating Terumah b'Shogeg or for benefiting from Hekdesh b'Shogeg.