Each member of the board of trustees shall be a qualified elector, and each member of the board of trustees elected from a subdistrict or a single-member district shall be a resident of the subdistrict or the single-member district of the special hospital district. The office of any member of the board of trustees who does not continue to reside in the special hospital district, and in the case of a member who is elected from a subdistrict or a single-member district, who does not continue to reside in the subdistrict or the single-member district, is automatically declared vacant.