Actually every twin engine commercial airliner built today can keep flying with one engine failed during pretty much every phase of flight.

It's actually worse from a yaw control standpoint to simply have one engine shut off during takoeff (rather than actually fall of the aircraft) because the drag that the failed engine creates adds to the yawing moment that the functioning engine on the other side creates. That yaw has to be overcome by the rudder and tail to keep the aircraft flying. If the engine simply fell off that drag goes away. All of this assumes that there isn't some larger structural problem with the wing of course.