Except as otherwise provided in the charter, reorganization does not affect any debts, demands, liabilities, or obligations of any kind existing in favor of or against the cities and the county, at the time of reorganization. Reorganization does not affect any pending action or proceeding involving any such debt, demand, liability, or obligation or any action or proceeding brought by or against any city or the county prior to reorganization. All such proceedings shall be continued and concluded, by final judgment or otherwise, as if reorganization had not been effected. All such rights or liabilities become the rights and liabilities of the city-county; provided, however, that the charter may provide for certain debts, demands, liabilities or obligations which are payable by assessments or ad valorem taxes on properties within a district or area (such as within a former district or city) to remain payable from such assessments or ad valorem taxes within such a district or area as though reorganization had not occurred.