According to the Fair Debt Collections Practices Act, if it’s past the statute of limitations for a creditor to contact you, you can send a follow up letter requesting that they no longer contact you.
You may still owe the money and it doesn’t mean the debt goes away. It just means that you can request that they no longer reach out to you and they must comply.
However, if the debt is sold to another collector, the process will have to be done all over again. It will only stop when you decide to go ahead and take care of your credit.