What would happen if any of my parents die and they have open credit cards accounts? There is no executor of the state since there are no assets or properties.
Do I, as the son, become responsible for these debts? Do I have to let them know they die?

NO, if you are not on the account, than you are not respondible for the debt.

Are you sure the estate would indeed have no assets? If when your parents die they have property of any kind - a checking account, a car, lwedding rings, furniture, pots and pans - then the estate has assets, and the estate must use these assets to pay off their debts, at least as far as they can. The executor (which may well be you) should indeed contact the credit card companies to let them know the account owner(s) are dead, and if there are any assets use them to pay them off. But you are not personally liable for the debts they have incurred.