There are beads attached to the draught excluder (draft dodger), which go under the door and are supposed to roll with any movement and keep the excluder flush to the edge. However the beads may not work well on carpets or doors with a threshold.
Make a draught excluder to block the gap under your door.
Got cold drafty air coming through your fireplace? Block it out by making a DIY fireplace draft stopper using this easy sewing tutorial. Using a draft blocker or door draft excluder also helps you to save on heating costs.