Depending on the table, I can see allowing the burning of 5 or 10 Karma to get a "Not Dead Yet" if you have no Edge left to be a workable rule.
To balance it, maybe it should be less effective than Edge, since you're relying on your karma rather than luck to save you, so you squeak by with even worse penalties than burning the Edge point, and it is only allowed if you otherwise have no Edge to burn.
Perhaps it even would reduce your maximum Edge to do it making it a more permanent "burn", not just using up your luck but using up potential future luck.
It depends on how the table plays, what kind of story the GM wants to tell and how much characters should be able to live through. It would fit better in big pink mohawk games and cinematic games, more than others.