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.
Trying to force a standard socket over a recessed BMW security bolt will wedging it tightly inside the wheel casing, massively increasing the difficulty and cost of professional extraction
BMW locking bolts are manufactured from heavy, hardened steel grades. Standard workshop drill bits will completely dull, slip off center, and permanently scar your premium alloy face.
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.