They will most likely send it to collections and / or a collection lawyer.
I will simply make myself the devil 's advocate here without really denying the fact that you did the work and that you were fired for money when the buyer challenged the prosecution. . But it's not as if the money was virtual, paypal ended up losing a few thousand dollars on this transaction. They must adhere to a number of rules, most of which are defined by credit card issuers, on how to handle litigation.
If this buyer was in your area, you can probably translate it into small claims court. If you can prove that all the work was done and that you stole $ 6,000, it would not be difficult to win.