No suit, action, or other proceeding lawfully commenced by or against any public officer in this state in his or her official capacity or in relation to the discharge of his or her official duties shall abate by reason of his or her death or the expiration of his term of office or his or her retirement, resignation, or removal from office. In such event the court, on motion or supplemental petition filed at any time within twelve (12) months thereafter, showing the necessity for the survival thereof, to obtain a settlement of the question involved, may allow the action or other proceeding to be maintained by or against his or her successor in office. The court may make such order as shall be equitable for the payment of costs.