What they do in is you get "Sand" in your "Hourglass". When you encounter stuff by which you should die, your "Time runs out". But when you do stuff that is interesting, you get more sand.
Getting injured counts as something interesting, which can earn you more sand and keep you in a fight that you were losing but think you can win if you just had more sand.
It's something that I thought was so interesting that I tried to incorporate it a bit in my game, Play it Cool. In play it cool, when you attack someone, your successes cause them a penalty on all future rolls, injuries in physical conflicts. But the injured character can make a soak roll as a normal stunt, and in Play it Cool, stunts are more likely to net successes based on how cool they are (detailed and awesome) so the more you describe the grissliness of an injury or how you narrowly avoided an injury by the skin of your teeth, the less likely that injury is to penalize you. I was going for the whole John McClain/Kung Fu movie thingie where you describe your own character's injuries, and since you describe them so horribly and it demonstrates how tough and awesome and committed to the struggle your character is, the rules let you keep fighting without too many penalties. That said, in Play it Cool, if someone shoots you with a gun, there is only so much that awesomeness can help you.
Anyway, in The Destiny System, you can also earn sand, what you call story points, by adding story, so it actually helps to save backstory for when you really need the sand. Or you can make up more backstory. Your knight's been taking it on the chin lately, well all of a sudden, you bust out in Latin. Oh you forgot to mention, he was a pilgrim in the holy land, and fought alongside the templars. Stuff like that earns you more lifespan. The downside is of course that if you are having an off day and this character just isn't catching your interest that night, you can kill off a character that you might have found interesting if you were in a better mood or had more time to think of cool things to do with him.