The starter cord on small engines is wound around a pulley inside the starter cover. This pulley houses a recoil spring that keeps the starter cord and pulley under tension. The starter cord won't retract when this spring breaks or gets ripped loose from the pulley. To solve this problem. you need to replace the recoil spring cassette. This spring can still be under a lot of tension, so wear safety glasses when installing or removing it.
Use the screwdriver to remove the screws holding the starter cover in place over the flywheel on your small engine. Take off the starter cover. On most small engines, the pulley and starter cord will be attached to the cover. Turn over the cover to work on the recoil spring.
Unwind the starter rope all of the way out of the pulley. Disengage the recoil spring from the pulley if it's not already loose. On most small engines, a small tab in the centre of the pulley can be popped up to release the tension. On others, you need to unwind the pulley by hand to release the tension.
Loosen the screw holding the pulley to the post on the starter cover. Take the pulley off of the starter cover. Use the end of the screwdriver to pop the recoil spring cassette out of the centre of the pulley.
Replace the recoil spring cassette with a new cassette. Put the new cassette inside the pulley. Wiggle the pulley back and forth until the end of the spring catches on the pulley.
Wind the pulley two full rotations clockwise. Wrap the starter cord around the pulley. Set the starter cover in place over the flywheel. Pull the starter handle and cord out about 6 inches. Screw the cover's retaining screws to tighten the cover in place.
Let go of the starter handle and it should automatically recoil. If it doesn't recoil, the spring isn't engaging the pulley. Repeat the process to ensure no mistakes were made. If the recoil spring still won't retract the starter cord, replace the pulley.
Recoil spring cassettes and pulley assemblies can't be repaired if they're broken. They need to be replaced.