Whenever the process of incorporation, consolidation, or annexation leaves a portion of a township with no qualified electors residing in that portion and without the constitutional and statutory officers to perform their functions as prescribed by law, as part of the alternate method of annexation provided for by section 9, a petition signed by the owner or owners of record or the holder or holders of equitable title under a recorded land contract or memorandum of land contract of all the real property of such portion of the township may be filed with the clerk of the city to which annexation is sought and with the county clerk of the county in which the territory is situated, seeking the annexation of such territory to such city. The annexation may be accomplished by the affirmative majority vote of the members-elect of the governing body of the city and approval of the majority vote of all of the members of the county board of commissioners.