If the debts are past the statute of limitations (SOL), the credit-card companies are out of luck. Even within the SOL, it would probably have to be a very large debt to warrant international pursuit. After the SOL expires, a creditor can pursue, but it's pretty toothless. If the debt is time-barred (after the SOL expires), they shouldn't be going after you at all. Some will, but there are things you can do to make it stop.