What happens if one party claims a settlement was finished out of court but is a lie?

What happens if "one party" claims a settlement was finished out of court but it is a lie? In fact, there was a settlement and the "opposite party" did abide by every agreement except for the full payment. However the "one party" doesn't want to go back to court because if they did let's just say they would be revealing a mistake they made on a large scale so they're letting the "opposite party" go. The "opposite party" is requesting proof of everything that was unfinished so they can go to court and claim that they haven't even finished paying.. thus the "one party" and their illegal scheme will be revealed. Howvever the "one party" is not handing over any papers. What can the "opposite party" do?
 
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