I'd probably leave too, but just because I wouldn't want to get stuck inside it if it stopped in the middle of two floors, especially since it was full. But for fear of death? Nah.
From Wikipedia: "In fact, prior to the September 11th terrorist attacks, the only known free-fall incident in a modern cable-borne elevator happened in 1945 when a B-25 bomber struck the Empire State Building in fog, severing the cables of an elevator cab, which fell from the 75th floor all the way to the bottom of the building, seriously injuring (though not killing) the sole occupant — the elevator operator. (...) In Thailand, in November 2012, a woman was killed in free falling elevator, in what was reported as the "first legally recognised death caused by a falling lift".
That's a pretty good safety record. Certainly much better than stairs.