(a) The term of office of a county administrator shall be four years and shall expire on the first Monday in March or when a successor is appointed and qualified. All vacancies in the office, whether by death, resignation, removal from the county, or removal from office, shall be filled by the probate court for the unexpired term.

(b) When the term of a county administrator has expired or when a county administrator has been removed from office, the county administrator shall nevertheless continue to discharge the duties of administrator of all estates remaining in the administrator's hands unless the letters of administration are revoked.

(c) A county administrator may resign the office as other administrators are allowed by law to do so.