I believe they're supposed to be able to land safely if the engine fails at almost any time. I don't think most runways are long enough to completely give them that luxury (if a plane lost power just before it had enough airspeed+altitude to circle back for a landing, I don't think there'd be anough runway left for a safe landing) but even there I suspect most planes will allow for a crash landing with a pretty good likelihood of the people surviving.
I should clarify: I believe one-engine planes are required to be controllable if the engine quits at any time, and should be able to land as safely as would be possible on available terrain.