If any part of the territory on which a sewer system is located, is taken into any city during the time any bonds of such sewage districts are outstanding, which bonds are payable by special assessments against lots or parcels of ground so taken into the city, the city shall be responsible for the maintenance and operation of the portion of the sewer system taken into the city: Provided, That the governing body of the sewage district shall continue to levy the special assessments against the lots or parcels of ground taken into the city which are necessary to retire such bonds. In the event of such annexation, the sewage district may continue to empty its sewage into any main, intercepting or outfall sewers in the territory annexed, and may continue to operate any sewage disposal plant in the territory annexed unless the city shall take over the operation of such sewage-disposal plant without charge to the sewage district: Provided, That if any sewers constructed by revenue bonds shall be within the territory so annexed, the governing body of the sewage district shall retain the right, after such annexation, to provide for continuation of collecting the charges herein provided for the use of such sewers in the annexed territory until such time as the original bonds or any refunding bonds issued to pay for such construction are retired, unless the city shall assume the obligation of the payment of the principal and interest of such revenue bonds as may then be outstanding.