Random example with arbitrary concrete numbers: let's say you owe $100,000 and you could afford to buy the debt for $1,000. However, that's also $1,000 available to pay toward your debt. If the creditor can be assured of getting that $1,000, then the debt is worth at least that much. And unless you're completely destitute with no prospects of ever earning any money ever again, it's worth more, because you'll have income with which to pay more in the future.
So in theory, if you can pay $1,000 to buy your own debt, somebody else should be willing to bid at least $1,001.
There's a lot that complicates this (expense and uncertainty of collecting assets through the legal system and such) but it's a thought.