Personally I don't think your dead until some undefined point when you can't be "brought back to life". I guess I put the line where your body as a whole begins to break down for whatever reason, be it bacteria in an appropriate atmosphere, the vacuum and radiation of space degrading the cells, or whatever. Its a hard thing to put a definitive line on as evident by the lack of a satisfying biological definition of "life" in the real world, much less a real definition of when someone or something is "dead". Either way, just how I've handled it in my rps, I'm sure others have done it other ways and have other definitions.
Your definition of death is a moving target with regards to advancing medical technology. Even today we can bring people back that 30 years ago we could not. Decay is just a kind of tissue damage, and bacteria feasting on your flesh is just a kind of infection. Death isn't an easy thing to spot per se either, and we have doctors declare people dead after attempts to revive someone fail. There's a certain point after which no oxygen to the brain will lead to unavoidable brain damage (today anyhow, perhaps in 30 years we'll be able to repair that and extend how long someone can be dead before being brought back). I'll grant my definition was imprecise, such as it is, as various parts of the body stop working at different points, but one might consider that just indicative that death has some grey areas.
In anycase, Jack goes through periods where his heart, brain, lungs, and so forth cease function and only comes out of that do to the fact he's a fact.
Oddly as it may seem though, defining "life" is different from defining "death," but that's because our definitions for "life" are very broad and involve reproduction ("life" and "alive" are different).
Anyhow, the game system seems to have a few ways to handle immortality of various sorts, which is pretty cool.