If a political subdivision that is not a member of an authority annexes real property that is served by the authority, the authority may continue to do business on and exercise jurisdiction over its properties and facilities over its annexed real property as long as:
(1) Any bond or indebtedness of the authority in effect at the time of the annexation remains outstanding or unpaid; or
(2) Any contract or other obligation of the authority in effect at the time of the annexation continues in force.