At issue is a flange on the end of the drive shaft “that was not produced with sufficient long-term durability characteristics,” according to the NHTSA report.
The connection between the driveshaft and flange can loosen over time, and eventually disconnect entirely. If that happens, then no power will get to the rear wheels, “resulting in loss of propulsion and increasing the risk of a crash.”
Which is typical NHTSA understatement for the possibility that your car will suddenly have no power, which is a terrifying prospect when you’re rocketing down the highway at 70 mph.
The fix is to simply replace the driveshafts with new ones. BMW has already narrowed down which vehicles are affected by this defect, so drivers should be notified with mailings saying whether or not they need to get their cars in for repairs.