W. Va. Code § 8-21-4: Filling vacancies.

When a vacancy occurs on said board by reason of death, resignation, change of residence from the city, failure to remain a freeholder of the city, or due to any other cause, the remaining member or members of said board shall appoint a successor or successors, or if there should be no members left on said board, the governing body of the city shall appoint successors, and in either event, the appointments shall be for the unexpired term or terms.