ולא אמרינן - כשזה תובע וזה אומר איני יודע אם לך אם לחברך אוקי ממונא בחזקת נתבע זה שלא נפסידנו ממונו ויהא מונח עד שיבא אליהו:
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If I understand correctly, the Mishnah is discussing a case where someone (Reuven) stole from one of two people (Shimon or Levi) but doesn't remember which is the victim. Shimon claims he's the victim, and Levi claims he's the victim. The Mishnah rules Reuven must give the full amount to both plantiffs.
The Gemarah notes that it seems that the court will take money from Reuven to give to each plantiff, even though there is doubt whether Reuven owes the money to each one. We do not say, "keep the money in the possession (chazakah) of the most recent owner [Reuven]."
Rashi explains that we are rejecting the following logic:
When this one (e.g. Shimon) claims and this one (Reuven) says "I don't know whether I owe you or your friend (Levi)," keep the money in the chazakah of this defendent (Reuven) so we won't make him lose his money (by paying both Shimon and Levi). Instead, leave the money until Eliyahu comes and determines whom to pay.
In other words, when we have a doubt about money, we often apply the principle of chazakah, that the money should stay by its most recent owner, and not take it away because of a doubt. So too here, when we don't know whether or not Reuven has to pay Shimon, we should let Reuven keep the money and not make him pay.