Children of an parent that has passed away are they entitle to pay the debt if no will has there. Such as personal property

I'm not sure what your question is based on the information you provided.  A child has no obligation to pay the debts of the estate.  If there was no will, you can still administer the estate because there is a law that governs who gets any assets even if the person dies without a will - its called Instestate succession.   If there is personal property in the estate, and needs to be distributed, someone has to be appointed to do that distribution and the personal property may have to be sold to pay the debts of the estate.