Eventually your debts would catch up with you as you can be traced any number of ways,a common way here in the UK is to trace your National Insurance Number,that never changes and is in use whether you work or are claiming benefits.
Who is going to track you through your NI number???
What about data protection?
I owed a large amount, moved house, left no forwarding address and no one has caught up with me 3 1/2 years later. The only people who could trace you through it would be a government agency not a bank or credit card company.