The governing body, at a regular meeting, may cancel and destroy all warrants drawn on any fund of the city which have remained on file for a period of one year or more next preceding the regular meeting at which the cancellation takes place. The governing body may cancel and destroy all warrants and checks which have been subject to payment and which have not been presented for payment for a period of one year or more next preceding such regular meeting. The governing body, before canceling and destroying any such warrants or checks, shall cause to be entered in the minutes of its proceedings a brief description of the warrant or check, containing the name of the payee, and the number, date, and amount of each warrant or check to be canceled and destroyed. If the party entitled to any such warrant or check, or to payment thereon, shall appear thereafter and give good and sufficient reason for that party’s delay in calling for such warrant or check or in presenting the same for payment, the governing body may issue to that person a new warrant or check in the amount to which that person is entitled, except for the statute of limitations.