When someone dies without a will, they are said to have died "intestate." Once all of a deceased person's debts have been repaid, state law will determine how any remaining assets will be distributed to heirs. A local court official, called a "surrogate" in many states, will appoint an estate administrator to handle settlement of a deceased person's estate.
This is often done in consultation with family members. You can only have an executor when there is a valid will. Administrators generally need to be bonded while they are managing the financial affairs of the deceased, which is an additional expense for the estate.
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