The powers which are conferred and the duties which are imposed upon any office or department of a municipal corporation under the laws of the state, or any ordinance which is in force on August 9, 1913, shall, if such office or department is abolished in pursuance of sections 705.01 to 705.92, inclusive, of the Revised Code, be thereafter exercised and discharged by the officer, board, or department upon which corresponding functions, powers, and duties are imposed under such sections. This section does not impair or affect the validity of any contract or bond executed or authorized prior to the adoption by any municipal corporation of one of the plans provided for in sections 705.41 to 705.86, inclusive, of the Revised Code. When any such contract or bond contains provisions that it shall be enforced by some officer, board, or department therein named, and where, by the adoption of any plan provided for in sections 705.41 to 705.86, inclusive, of the Revised Code, such office, board, or department is abolished, the powers conferred and the duties imposed with reference to the officer, board, or department shall thereafter be exercised and discharged by the officer, board, or department upon which like powers, functions, or duties are conferred or imposed under sections 705.01 to 705.92, inclusive, of the Revised Code.