It shall be the duty of the court clerk receiving any costs or fees belonging to any other person, to deposit the same in the court fund subject to the order of the person entitled thereto, and to pay the same over on request; and if such costs or fees shall not be claimed by the end of the fiscal year following the fiscal year of receipt, except in all cases where jurisdiction is continuing, and by the end of the fiscal year after the year in which final judgment is granted, they shall become the property of the court fund, provided that any unexpended court costs or money belonging to litigants shall be mailed by the court clerk to the proper attorney of record.