If after both the normal filing period and special three-day filing period as provided by RCW 29A.24.171 and 29A.24.181 have passed, no candidate has filed for any single city, town, or district position to be filled, the election for such position shall be deemed lapsed, the office deemed stricken from the ballot and no write-in votes counted. In such instance, the incumbent occupying such position shall remain in office and continue to serve until a successor is elected at the next election when such positions are voted upon.