If any special assessment or special tax before January 1, 1942 has been, or on or after January 1, 1942, is annulled by the corporate authorities, or set aside by any court or declared invalid or void for any reason whatsoever, a new assessment or tax may be made and returned and like notice shall be given and proceedings had as required in this Division 2 in relation to the first. If any local improvement before January 1, 1942 has been, or on or after January 1, 1942, is constructed under the direction of the board of local improvements and has been or is accepted by that board, and the special assessment or special tax levied or attempted to be levied to pay for the cost of such an improvement has been or is so annulled, set aside, or declared invalid or void, then a new special assessment or special tax may be made and returned to pay for the cost of the improvement so constructed, or to pay for the cost of such part thereof as the corporate authorities might lawfully have authorized to be constructed and paid for by special assessment or special tax. All parties in interest shall have like rights, and the corporate authorities and the court shall perform like duties and have like power in relation to any subsequent assessment or tax as are provided in relation to the first.