As I said, dropping below zero kills them. Dropping to (apparently) zero, but not below it, does not kill them. Outside of that not-particularly significant detail, health does exactly what you expect health to do.

Note that there's no way to tell exactly how much health they have; the health bar, like the skill bar, changes in increments, and nobody who knows is saying exactly how that is tracked or rounded, though I could likely find the value with an external utility, if anybody really cared. I don't see that it would help me play the game, though, to know if an empty health bar is really a zero, or just 1 out of 100 health points, rounded down to the closest increment on the health bar.