No special assessment or special tax shall be held invalid because levied for work already done, if it appears that the work was done under a contract which has been duly let and entered into pursuant to an ordinance providing that such an improvement should be constructed and paid for by special assessment or special tax, and that the work was done under the direction of the board of local improvements and has been accepted by that board. It shall not be a valid objection to the confirmation of this new assessment that the original ordinance has been declared invalid or that the improvement as actually constructed does not conform to the description thereof as set forth in the original special assessment ordinance, if the improvement so constructed is accepted by the board of local improvements. The provisions of this section shall apply whenever the prior ordinance is held insufficient or otherwise defective, invalid, or void, so that the collection of the special assessment or special tax therein provided for becomes impossible. In every such case, when such an improvement has been so constructed and accepted, and the proceedings for the confirmation and collection of the special assessment or special tax are thus rendered unavailing, the corporate authorities shall pass a new ordinance for the making and collection of a new special assessment or special tax, and this new ordinance need not be presented by the board of local improvements.