You should never let your car run out of AdBlue. If it does, the engine will go into ‘limp’ mode, which drastically reduces power to keep NOx emissions within legal limits. If that happens, a warning will appear on the driver’s display and you should refill the AdBlue tank as soon as possible. You should also avoid turning off the engine until you have access to more AdBlue, because the engine is unlikely to restart.
Incidentally, running out of AdBlue is just one of many reasons that an engine will go into limp mode. Any severe problems with the engine or gearbox that occur while driving will activate limp mode. It’s there to prevent further damage and keep the car moving so you can stop in a safe place to call a breakdown service, or quickly get to a garage.