For the sole and exclusive purpose of winding up the affairs of a dissolved special purpose district, the county legislative authority, acting as a board of trustees, shall have the same powers and duties as the governing authority of the dissolved special purpose district including the following:

(1) To exchange, sell, or otherwise dispose of all property, real and personal, of the dissolved special purpose district; and

(2) To settle all obligations of such special purpose district. Such powers and duties shall commence upon the effective date of dissolution and shall continue thereafter until such time as the affairs of the dissolved special purpose district have been completely wound up.