Whenever an improvement contract has been awarded, the county or city or district or other public corporation, the legislative body of which is conducting the proceeding, shall, if the actual cost of the improvement, including incidental expenses, exceeds the amount that may be specially assessed upon benefited property, pay such excess cost from the general or any fund available and the balance shall be specially assessed under the statute under which the proceeding is conducted.
If the property to be specially assessed is within the jurisdiction of more than one legislative body and consents to such proceeding have been given by all the legislative bodies having jurisdiction, any such legislative body whose consent has been so given may appropriate all or any part of such excess cost from any available funds under its control, and may pay the amount so appropriated into the treasury of the county or city or district or other public corporation whose legislative body has jurisdiction over the proceeding to be applied in payment of such excess.