The Gemora answers: He understands the verse is required for the teaching of Rava bar Ahilai, for Rava bar Ahilai says: Why does Rav say that if a person admits to a fine (which a person by Torah law does not have to pay based on his own admission) and then witnesses come and testify to his guilt that he is still exempt from paying? This is as the verse states, “If it will surely be found.” This teaches us that if it was first revealed with witnesses he should then be decided as guilty by the judges. This excludes a case where he admitted his guilt. [He will be exempt from paying the fine even if witnesses come later.]
Does this ruling apply only in the Beis Din in which the person admitted to the fine, or does it apply even where witnesses testify in a second Beis Din against him?
The Ketzos Hachoshen (350:2) writes that when one is exempt from liability after admitting to a fine, it is not as if the obligation is cancelled; rather, the halachah is that Beis Din cannot obligate him to pay after he has incriminated himself. Therefore, the exemption applies only in the Beis Din in which he admits. If, however, he admitted in one Beis Din and afterwards he was sued in a second Beis Din and witnesses testified against him, the second Beis Din may obligate him to pay the fine. And similarly, if witnesses testify against him in one Beis Din but they did not complete the judgment, and then he is taken to a second Beis Din where he admits to the fine, he will be exempt from paying, since witnesses had not testified in the Beis Din where he admitted, and the Beis Din where he admitted cannot make him liable, for he incriminated himself.
The Nesivos Hamishpat disagrees and maintains that once a person admits to a fine in one Beis Din, he no longer can be obligated to pay even if witnesses testify against him in a different Beis Din. He also holds that in a case where witnesses testify against him in one Beis Din but they did not complete the judgment, and then he is taken to a second Beis Din where he admits to the fine, the second Beis Din cannot obligate him to pay, but it is not because the halachah of admitting is dependent upon Beis Din. Rather, it is because that as long as a verdict has not been reached, it is still regarded as a fine, and therefore, if he admits before a second Beis Din, they cannot obligate him to pay, for he has incriminated himself. However, if witnesses will testify against him in the second Beis Din, he will be liable to pay.
The Nesivos evidently holds that once he admits to the fine and is exempt from paying, the debt is completely cancelled and a second Beis Din cannot make him liable to pay any longer.