One problem related to engine shut off without warning has been reported for the 2011 BMW 335. The most recently reported issues are listed below.
Engine shut off loss of power steering loss of ability to accelerate while driving on 7/27/17, our 2011 BMW 335i's ability to accelerate stopped, rpm increased but still in drive not in neutral. During loss of accelerate, power steering failed and was unable to pull off side of the road. This happened while vehicle was in motion on a busy city street. Had to put on hazards in middle of street.