If on the first Monday after January 1 following a general election the person elected to an elective county office has resigned or died, the board of supervisors shall provide that the office which was made vacant shall be filled at the next regularly scheduled election. The board of supervisors may appoint a person to temporarily carry out the duties of any office to be filled by such an election and that person shall serve until the results of the election are declared.

The person elected shall serve for the remainder of the term which began on the first Monday after January 1 immediately preceding the election.