Most wills have a clause that waives any bonding requirement that an executor is required to post before assuming the executor role. The executor has the power to encumber the estate with reasonable debt in order to pay expenses that can be used to improve the estate's value. If the executor is acting in the estate's best interest and does not breach a fiduciary duty, he is then not personally responsible for any debts owed. If the estate has few if any assests or money, then the executor should contact the creditor's directly and explain the estate's condition. In most cases, creditors will greatly reduce the amount owed or they may even write-off the debt. Either way, the executor is not responsible for any debts pre-dating his appointment and is not liable for any debt that is encumbered to improve the estate as long as he is not breaching any fiduciary duties.
Q # 1: Executor's liability for Decedent's debts. Simple answer: The Personal Representative of a Decedent's estate (Executor with a Will or Administrator without a Will) is liable, in his or her fiduciary (but not individual) capacity, to pay the Decedent's taxes & debts, up to the limit of Decedent's assets. If the assets are insufficient to pay the estate's espenses, taxes, & debts, the estate is insolvent and is ineligible to be granted Nonintervention Powers, meaning that all major actions taken by the Personal Representative will require prior Court approval.
Q # 2: Payment of expenses, taxes, & debts in an insolvent estate. Simple answer: The payment of an insolvent estate's expenses, taxes, and debts is made by "ranking" them according to a priority order (see RCW 11.76.110) and then paying each successive rank until insufficient funds are available to pay all items within that rank, in which case those items are paid ratable, so many cents on the dollar. The ranks, in decreasing priority order, are shown in Paragraph C at: