Run-flat tires are designed with reinforced sidewalls that allow the tire to be driven for a limited distance without air. Some run-flat tires can be plugged, if a patch is placed over the plug.
Manufacturer recommendations about repairing runflats vary. Some manufacturers specify what sort of damage to a run-flat can be repaired. For example, Goodyear recommends repair only if the damage is within the tyre's outside grooves and restricted to the tread. The company also specifies that plug of 1/4-inch in diameter be used, with a patch applied over it.
Some manufacturers recommend that run-flats with splits should be replaced, and that repairing them will void their warranty. If the fabric of the tire has split, repair might still be possible, but it will be more complicated and the speed rating of the tire will be lost. This means it should not be driven beyond normal highway speeds.
Many tire shops refuse to repair run-flats. Most car manufacturers still use conventional radials and not all tire dealers even stock run-flats, so there may be a wait of a few days if you need to replace a run-flat tire.