They are limit straps. They limit the droop to keep the coil from falling out and/or so the shock isn't the limiter. Using the shock to limit droop can cause the shock to fail.
They are usually found on desert race trucks. These truck see lots of air time. When jumping a vehicle, the axle will droop/fall fast which can literally yank the shocks off the rig.
Usually they are not needed on a rig that unloads the shocks slowly, like a rock crawler.
If you need the straps, they stay on all the time, on and off road.