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.)