All political subdivisions, agencies of the State, and municipal and quasi-municipal corporations may make agreements with the board obligating themselves to do or perform those things which are required of the State, political subdivisions thereof, or other local agencies by the act of Congress approved June 22, 1936, or any acts amending or adding to it, now or hereafter adopted.
When an elimination, modification, or alteration of any authorized plan of flood control is made at the request of a political subdivision, agency of the State, or municipal or quasi-municipal corporation, the political subdivision, agency of the State, or municipal or quasi-municipal corporation may, in agreements made pursuant to this section, assume responsibility for all claims of damage or liability made against the State and its agencies or the United States and arising from the requested elimination, modification, or alteration of the authorized plan of flood control.