Sure they will. Why? Because every time you make any payment whatsoever or say or do anything to acknowledge the debt, the statute of limitations on suing for the debt gets restarted. Unless you have an intention of paying off the debt in the short run, do not make any payment and say nothing that could be interpreted as your agreement that the debt exists.
I am sick and tired of this number calling and calling me. I get calls at 8:06am on a SUNDAY. My only day off!! This is in regards to my Victoria Secret credit card that I paid and I told them I paid. I don't have time to pick up and talk to these [***]. They call no less than 6 times a day. This has got to stop!!!!!