(a) If any township refuses or neglects to organize and elect township officers, the county board of the county may order another election for that purpose at the time of the next regular election scheduled under the general election law. The county board shall appoint qualified residents of the township to serve in the township offices and to perform the duties and possess all the rights and powers of those offices until the regular election of officers provided in this Code.
     (b) If the township does not then organize and elect officers, the county board may, at any regular or special meeting, appoint the necessary officers for the township. The persons so appointed shall hold their offices until the next annual township meeting and until their successors are elected or appointed and qualified.
     (c) If the persons appointed under subsection (b) fail to qualify as required by law or if, at any time after the organization of the township, the electors of the township refuse to elect or appoint officers or to exercise the powers required by law, the county board may annex the township to an adjoining township. The township so annexed shall thereafter constitute a part of the township to which it is annexed.