Pursuant to this section, the board of trustees may find and declare that the authority shall cease to exist. In that event, the board of trustees shall provide for the disposition of the authority’s assets, obligations, and liabilities. Absent written agreement, the county shall not be obligated under any law to assume the authority’s obligations or liabilities, or take title to, or custody or control of, the authority’s assets. Upon notification by the authority of the disposition of the authority’s assets and liabilities, the board of supervisors shall rescind the ordinance that established the authority, and the authority shall cease to exist on the date set forth in the rescinding ordinance.