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They can try to collect from you, but you are under no obligation to pay.
I suppose CapOne could decide to close your account/rate jack you etc.
There was an article a few months ago in the NY Times (I think) on a very profitable collection method. These collections agents were calling relatives of recently deceased people basically guilting them into paying the debts of their relative. Surprisingly (to me), many people end up feeling guilty enough to pay.