Funny enough, I wrote about debt collection in an HN comment recently. The most important thing to remember is that if you defaulted on a debt AND that debt has already been sold to a third-party collector, then you actually have NO incentive to pay the debt collector. At that point, the debt has already been written off the creditors books, so not a dime of the payment goes back to them. Further, if the debt resulted in a black mark on your credit history, paying it back will not erase it. Debt collectors cannot "fix" your credit rating.
The only thing that paying a third-party debt collector will do is stop them from calling you. Possibly.
(If a debt collector is hounding you about a debt you never legitimately owed, pretty much every state has a procedure for rectifying that. And the punishment for a collector not cooperating on said rectification is you get to sue them if they don't.)
Also: Everyone (including myself) has been talking about unsecured debt, but it may be worth mentioning secured debt as well. I once had an interest in buying real estate notes (mortgages, essentially). It turns out these are bought and sold for some percentage of face value all the time. The amount of the discount depends on the status of the mortgage payments, the balance of the loan, and the reason for the seller looking to unload it. When buying notes, there are multiple exit strategies but the most profitable one is often to work with the home owner to restructure payments in order to "rehabilitate" the loan. Meaning, the owner gets to stay in their house, possibly with a more favorable payment, and the investor gets to keep a performing note, or sell it to a more conservative investor.
The only thing that paying a third-party debt collector will do is stop them from calling you. Possibly.
(If a debt collector is hounding you about a debt you never legitimately owed, pretty much every state has a procedure for rectifying that. And the punishment for a collector not cooperating on said rectification is you get to sue them if they don't.)