One of the first concrete examples of a 767 flying on one engine came shortly after the aircraft type was introduced into the world's airline fleets. And actually, it flew on no engines! The well-known story of The Gimli Glider involves an AC flight from YYZ to YEG which was fueled incorrectly, confusing metric with imperial. This meant the plane ran out of fuel half-way along its flight path. The pilot recalled a landing strip in Northern Manitoba and managed to glide the aircraft onto that strip, somewhat surprising a group of residents who were having a day of drag racing on the up-to-then abandoned runway.
Two months ago, a two-engined A330 ran out of fuel -- due to an unfastened valve -- over the Atlantic. Forturnately, the pilot was able to glide it onto a runway in the Azores.
ETOPs rules require twin engined jets to be able to fly for a certain amount of time on a single engine, in order to make land when crossing oceans.
Under "normal" engine loss circumstances, it would be the catastrophic loss of an engine, accompanied by a structural failure -- as appears to have occured today -- that makes the aircraft unstable and could pose problems of control of flight surfaces.