One problem related to engine stall has been reported for the 2007 BMW 335. The most recently reported issues are listed below.
While driving on the hov lane of the freeway during rush hour about 5:15 pm my car suddenly started to rattle when pushing the gas paddle. I took my foot from the gas paddle while still driving with about 60 mph. I tried the gas paddle some seconds later again and experienced still rattling and no acceleration of the car. I took my foot again from the gas paddle. In the meantime I was down to 40mph. About 20-30 sec later from the first rattle the engine light came on and 1 sec later the engine stalled on the highway. At that time when the engine stalled I was still driving about 35 mph. Luckily the freeway had a left shoulder and I turned over to the left with the last remaining speed and slowly stopped the car. I'm so glad that the left shoulder was available. The freeway was very busy and I assume I would have been involved in an accident, if the left shoulder wouldn't have been available. The loss of power was too sudden and entirely unexpected. The stalled engine created a very dangerous moment while driving on a freeway. The BMW shop came back to me today and explained that the high pressure fuel pump failed. A know issue with the car make, model and year.