I would rule that ANY time the character dies he can use a FP to be Left for Dead. This does present certain problems, of course, depending on HOW the character died --
DM: You slip off the deck of the pirate sloop and into the water. Your heavy armor drags you inexorably to the bottom of the ocean where you become fodder for bottom-dwelling monsters of the deep.
Player: I burn a fate point to be Left for Dead.
DM: Er... uh... um... Okay, I guess you manage to get the armor off and your apparently lifeless body floats to the surface. Yeah, that's it.
The other problem, totally unaddressed by the rules, is that of scarring. If a character dies in a fire and uses a FP to be left for dead, would he really come out of it the same person he had been before?