The county legislative bodies are empowered to levy a special tax within the territory embraced within the limits of any incorporated town or city whose charter has been abolished and no new charter granted, or no reincorporation has taken place, or when a new charter has been granted making no provision for the indebtedness of the former corporation, for the purposes of meeting existing indebtedness due, meeting annual or semiannual interest charges on bonded indebtedness, providing any required sinking fund, and paying off all indebtedness when due.