Any officer of the city may resign from office. If such officer resigns he or she shall continue in office until his or her successor has been chosen and has qualified. If there is a failure to appoint a city officer, or the person appointed fails to qualify, the person filling the office shall continue in office until his or her successor has been chosen and has qualified.
(65 ILCS 5/3.1-10-50) (1999 Code, § 1-2-23)