And in the real world, this is a solution that does occur. There's the term "Paid in full", meaning the debtor has paid off the entire debt. There is also a term "Paid As Settled", meaning the debtor and the creditor have agreed that a portion of the total debt will be paid, and will settle the whole thing.

Usually, the debtor has to make the first move, contact the creditor and basically say, "Hey, we know we have this debit and we want to take care of it...but here's our situation...can we work something out?" 9/10...an agreement can be reached.