Statute of limitations laws are somewhat vague, so while most credit cards are considered "open accounts" some cases have filed suit as "written contracts" apparently
SC has a 3 year statute of limitations on open accounts, but 10 years on written contracts. Until/unless you get a subpoena though, they are probably just trying to intimidate you into paying. If you make even one payment, the SOL starts over. I would tell them flat out the statute of limitations has run out and see how they react. They are usually counting on you being uninformed.
Bud Hibbs Helps America Hold Debt Collectors to the Law!