I've been playing the cumbersomely titled Final Fantasy XIII-2 on the PS3 (or as I call it, since it's full of tedious and improbably dressed pseudo-Californian teenagers emoting about their tedious fucking "issues" - Final Fantasy XIII-90210).
In the same fashion as it's predecessor FFXIII (or as I call it, Advanced Corridor Walking Simulator) the party restore all their HP after each and every combat. That seems a bit radical to my eyes but...
It might be a good idea for a D&D variant.
Yeah, it goes totally against the grain of D&D as a resource management game and seriously cocks up the balance, mathematics everything.
But, if the game had done this since day one, with the inference that Hit Points were "survival under fire in a single melee" as opposed to "survival under fire in the dungeon as a whole" then nobody would bat an eyelid at it and it would probably be the standard for every RPG mechanic that broadly equates to "Hit Points". Both approaches are somewhat abstract, it's just one of them is the abstract approach originally employed and obviously the other one, err, isn't.
You could even add a bit of Old School flavour to this by rerolling HP before every battle which would shake things up a bit.
FFXII-90210 adds a bit of grist to the mill in something it calls a Wounding attack. This wounds and lowers maximum hit points at the same time. Max HP is restored after the battle. So, if Gorgan M'reywolf(*) has 12 hit points, suffers 4 hp from a so-called "Wounding" attack, 3 hp from a normal attack (down to 5 hp, remedial level maths fans) and then is Cure Light Wounds-ed by Dead Aleena during the combat, she only gets healed up to 8 hit points. After the battle she auto-heals to 12 as normal. So far in FFXII-90210 I've fought a boss monster with this ability but I'm not sure why he has it and others didn't.
Perhaps this could be recast as a Poison attack - so that a attack with a Save vs Poison element is "Wounding" damage if the save is failed otherwise the damage is straight hp loss. (i.e. a spider or snake does it's bite damage on a successful Save and the same damage as "Wounding" if the Save is failed. Or you could take a leaf from the Final Fantasy games and have a continual drip-feed of damage from a poisoned attack equal to the monster's HD every round until cured, dead or the combat is over. This would replace Save or Die in this instance.)
Of course, this ignores damage from non-combat sources such as traps. Perhaps the solution here is to beef up the nastiness of traps and then auto-heal after the trap encounter is resolved. So either the trap does enough damage in one blow to kill the PC or, put simply, it just doesn't and the PC gets away with it.
(*) Back in the mists of pre-history we used to name characters in this fashion quite a lot. Take a famous fictional name and flip the first characters or syllables of each name which led to PCs with names like Greydalf the Gan, Melric of El'Nibone, Goonmlum, Ford Loul and Bonan Carbarian.