The position you are think of is when the card co. make no effort to contact you for six (I think) years. When they have sent correspendence to your registered adress and then tried to follow it up they will get you in the end.
Its six years if you can prove there has been not contact at all. You may have unwittiingly acknowledged the debt eg by phoning your provider during that time or asking for your credit record. The debt may also follow you around if you try to get credit.