A plastic can liner and a drawstring for closing the can liner. First and second plastic panels joined along edges of the panels define a bag body. Opposed first and second panel edges that are not joined define a can liner opening. A first hem extends along the first panel edge and a second hem extends along the second panel edge. A drawstring extends through the first and second hems. The drawstring is a cross-laminated plastic film. In some embodiments, the drawstring includes first and second drawstring strips sealed together adjacent the opposite ends thereof. Each of the first and second drawstring strips can be made from a plastic film including a first layer and a second layer bonded to the first layer. Each of the first and second layers have a machine direction oriented transverse to the length of the drawstring and the machine direction of the other layer.