In all cases where any sheriff, constable or coroner has executed any writ or other process delivered to him or her by his or her predecessor, or has completed any business commenced by his or her predecessor under any writ or process, and has completed any other business commenced by his or her predecessor, and in all cases where any sheriff, constable or coroner has executed any writ or other process, or completed any business connected with his or her office after the expiration of his or her term of office, which writ or process he or she had commenced to execute, or which business he or she had commenced to perform, prior to the expiration of his or her term of office, such action shall be valid and effectual for all purposes.