Except as otherwise provided in section 31-543, all lawful claims, rights, and demands against such a district, and all contractual obligations of such a district, existing in any person at the time of discontinuance of the activities and work of such district, shall continue to subsist in such person and shall remain the charge and obligation of the sanitary district, and all claims and demands in favor of such district at the time of the discontinuance of its activities and work shall subsist in its favor and may be collected in the same manner as might have been theretofore done by the district.