Commentary for Kiddushin 126:4

The father does not remember to whom he betrothed his daughter. At this point she is in a terrible situation; she could be married to anybody therefore she is forbidden to everybody, lest she be married to someone else. Comes along a man and says that he was the one who betrothed her. He is believed, since there is no contradictory testimony.

In this case two men come along and claim that they are the ones who betrothed her. Neither can marry her lest she is betrothed to the other. They must both give her a get. However, if they come to an agreement, one may give a get and then the other may marry her.