Oregon Revised Statutes Cities § 221.160

(1) Whenever because of death, resignation or other cause the number of the members of the governing body of any city is insufficient to constitute a quorum for the transaction of the business thereof, and the charter of such city does not otherwise provide, the mayor, or if there is no mayor, a majority of the remaining members of the governing body, may call a special election for the purpose of electing a sufficient number of persons to fill all the vacancies then existing in the governing body. For the purposes of such election the mayor, or if there is no mayor, a majority of the remaining members of the governing body, may appoint persons to act for all offices necessary to the holding of such election where such offices may be vacant. The appointments shall continue until a successor is selected as provided for by the charter or law governing such city.

(2) If all positions in the governing body of a city become vacant and if the charter of the city does not provide otherwise, the governing body of the county in which the city maintains its seat of government immediately shall appoint the number of persons sufficient to constitute a quorum for the transaction of city business. The persons appointed by the governing body of the county shall appoint a sufficient number of persons to fill any remaining vacancies existing in the governing body of the city. All persons appointed under this subsection shall serve until successors are elected and qualified to serve.