A twin-engine airliner CAN safely fly if an engine falls off (or just quits) provided the wing / flight controls are not damaged too much and the crew performs correctly (UA almost lost a B747-400 last year when one engine failed on takeoff at SFO. The crew did not use correct flight control inputs and nearly hit the hills to the west of the field). The pylons (what the engine is mounted to) are designed to "break-away" from the wing cleanly - this could be caused by severe turbulence, an un-balanced engine, internal damage, bird strike or any number of situations.

As part of our training, we practice engine-out manuevers numerous times during our semi-annual simulator sessions. Granted, we don't practice an "engine falling off". However, we do practice hydraulic system failures (single, dual, and complete failures - like UA232 at SUX), fires, electrical system failures, flight control failures (flaps, slats, rudder, elevator, trim and even complete flight control failures), etc. We even practice multiple system failures at the same time.