The board may provide for the execution and authentication of bonds by the manual, or by lithographed or printed facsimile, signature of officers of the board and by additional authentication by the county treasurer as trustee. If any of the officers whose signatures or countersignatures appear upon the bonds or coupons cease to be officers before the delivery of the bonds or coupons, their signatures or countersignatures are nevertheless valid and of the same force and effect as if the officers had remained in office until the delivery of the bonds and coupons.