Since the probate process requires someone to act on the behalf of the estate, if an executor dies and there is no co-executor or named successor executor, the court will appoint a new one.Typically, someone interested in the estate petitions the probate court for appointment. Preference is given to immediate family members (e.g. the surviving spouse or adult child). If a family member does not want the job, they may be permited to choose someone else for the job.