If you choose not to spend them, what happens?
Well, going by the description [MENTION=67296]Laurefindel[/MENTION] provided, I'd say that the attacker gets to succeed. Meaning if the attacker is trying to kill you, you die.
What a really fantastic way of modeling HP. Consider that yoinked. I LOVE that interpretation. It makes HP actually make sense. It's a player resource that they spend to avoid negative consequences. Which means that you could easily model just about anything you want to model.
Such as, say, a duel where the goal isn't to kill the other, but, rather, to the first hit. Nobody actually scores a hit until someone runs out of HP. Or, if the PC falls off a cliff and doesn't die, it's because there was a tree sticking out that broke your fall, placed there by the expenditure of HP.
Wow. I can see this being a fantastic way of running the game. And, as far as something like a poisoned weapon goes, well, sure, you can avoid the HP ablation of the weapon, but, the poison effect is separate, so, because of the poisoned weapon, you are somewhat constrained in how you spend your HP to avoid effects. No different than you can only avoid half of a fireball in a saving throw, not the whole thing.
Sure, there might be some wonky corner cases, but, that's always going to happen when using HP. But, this, unlike virtually every other interpretation I've ever seen, actually works the most often.