There are several ways a BMW locking wheel nut key can fail, but this is one of the most common and frustrating scenarios. As shown in the image, the unique pattern that engages with the locking wheel bolt has completely snapped off the key. Once the key's internal teeth or "flower" pattern shears off, any remaining locking bolts on the car—typically one per wheel—are now effectively "stuck".
This is a less-than-ideal situation! Where a broken piece of the key remains wedged inside the bolt head itself. Different methods for removal are required for this but a good locking wheel nut removal specialist will make short work of it. You might get lucky and get this snapped part out but it’s not critical.
Locking wheel bolts are generally made from much harder steel than mild steel. Poor drilling technique or the wrong tools can cause the bolt to work harden, making removal almost impossible without professional grade tooling.
Chisels:
Hammering a chisel into the bolt might seem like a good idea, but the chance of successful removal is low and the risk of damaging the alloy is very high. Once the wheel is gouged, the repair can end up costing far more than the original problem.