Technically, a debt collector can come after you forever for defaulted debt...however, once the statute of limitations is up...they've lost the power to successfully take legal action. Per the Fair Debt Collection Practices Act, you can send them a "cease communications" letter and that will be all that you need to do. Per this law they must cease collection activity.
Send the collection agency a letter via Certified Mail + Return Receipt (NOT regular mail) stating:
Per the Fair Debt Collection Practices Act, cease all communications with me about this alleged debt.
This letter has been mailed via Certified Mail with Return Receipt. Receipt of this letter is being officially time stamped. ==========================
* DO NOT sign your signature on any document that you mail to a debt collector. It could end up on a forged document that can be used against you. Simply type your full name.
If the debt collector calls back, tell them that you have officially sent a certified letter to them to cease communications with you per the Fair Debt Collection Practices Act. Don't let them scare/bully you into paying this ancient, time-barred debt with bogus threats of arrest or legal action...they can't do either...they are powerless over you.