(Q

Is there a limit to how long a creditor can try to collect a debt?
(A

Yes and no. Every state has a statute of limitation on the legal ability to enforce a debt by suit.
Many states are 7 years, while some states are as little as 3 years.
Creditors can bring suit anytime within that period. But, should they attempt to bring suit out of the statute of limitation, the key is always the fact that your defense (that you are beyond the statute of limitation) must be raised.
Therefore, you could conceivably be sued after the statute runs out, and if you do not raise the statute as a defense, you could loose.
The key to the defense is proving you did not acknowledge the debt since the clock started. One $10 payment or a promise to pay can start the clock over.
That being said, once a debt always a debt. Therefore, a creditor can pursue collection activity forever and simply become annoying. Therefore, it is usually a good idea to settle your debt if possible.
While they may not prevail in court after the statute runs out, they may still be a thorn in you side. So to that end, if you are dealing with a large debt and you get sued after the statute runs out, it may actually be in your favor to go to court and raise your statute defense, because if you win the case and the judge rules in your favor - case closed. It is unlikely the creditor will pursue further collection action - because they have no where to take it legally by sueing you.