You legally owe debts until it is paid, settled or it is wiped off by bankruptcy filing (if you do file for bankruptcy). Even if your debt has been charged off or if your creditor cannot report it because if has gone past the statutes of limitation, you still technically are in debt. Your creditors can still come after you. Morally, one could argue that it is possible, you should pay off your debts when you can. And this seems to be a fair statement.
However, paying off old debts can actually hurt your credit scores. Why?
1. The credit bureaus weigh recent activity more than old activities. If and when your creditor or collection agencies update your report, this may hurt your score and you may be better off not doing anything.
2. Any action like contacting your old creditor or even acknowledging your old debt can land you in court. Some states have laws that allow the statutes of limitation to be extended if you make a payment to your old debt. You could be taken to court by your creditors and any judgement against you would be serious implications on your credit report.
But there may be another reason why you should never bother or acknowledge any debt past the statutes of limitations. More often than not, you will be dealing with collection agencies. And they could be very unpleasant to deal with.
So morally, it paying off your old debts seems like the right thing to do. But in reality, it is actually more complicated than you think because of the laws and how credit bureaus actually work.