Hitpoints are a metacurrency.
GM: The orc stabs you through the chest with its sword, you die.
Bob the Fighter's Player: Oh, I don't like that, I'll spend my hitpoints to prevent that.
GM: Okay, spend <clatter> 7 hitpoints.
Player: Okay, I had 10, so I have three left.
GM: Cool, the orc stabs at you but you manage to twist out of the way at the last minute and only take a shallow gash across your ribcage. The second orc swings his mace and <clatter> smashes your skull in.
Player: Um, hitpoints, again?
GM: Sure, spend <clatter> 5.
Player: Gulp, I only have 3.
GM: Okay, you drop to 0, and you die, crushed skull.
Player: Oh, wait! I invoke dying!
GM: Sure thing, you drop to zero, the mace has struck the crown of your head, but whether or not it was a fatal blow or a glancing one is yet to be revealed, make a death saving throw!
Player: Yes! <clatter> NO! A 1.
GM: That's two saving throw fails, looks like it's getting close to curtains!