No - Next of kin are not responsible for the debt, the debt goes against the estate,if the estate is insolvent, the estate is administered as if in bankruptcy.
If you think about it it would be absurd for you to inherit problems from someones financial mismanagement. If you did not like your kids you would just rack up huge debts as you got older and leave them and their families to clean up the mess. This would make not sense whatsoever.
