So there seem to be two rival camps that will never see eye to eye on this. 1) Those who prefer the way the EU editions didn't allow death saves... no elixir of life, no last minute potion or healing spell, when you reach body points of zero you are D-E-A-D and your character is removed from play (well, unless you're playing the Dark Company, perhaps)... and 2) Those who favor the NA/Remake way of doing things, where you can save yourself with your own healing ability or item, and they only quibble over exactly which ones count and when (like can you use a healing spell if you were killed on Zargon's turn? some say yes, others say no, or witness the recent Wandering Monk discussions about his Twisting Torrent ability to avoid damage, etc). The Japanese edition handled it differently (and some great threads on that if you wish to search for them). This debate over which is best will never die (pun intended) and that's fine.
But what about this? I played at a table where a volunteer for Avalon Hill (from another game company) was playing it so that if your hero died you were NOT allowed to save yourself from death, period. (if anyone else was there, it was KnightFall at the 2023 convention).
However what he did do was have it so that the character is simply "down" or "bleeding out" and you had until the end of the hero's round (or the next hero's round if you were the last hero in line if I recall correctly) for any ally to walk adjacent to your character's "body" (we tipped the mini over on the square where they "died") and then apply their healing potion or spell to revive the character.
This sort of thing should be familiar to many players of video games released in the late 2000's to today (well I can't say today because I am not up to date on the latest console games that are popular, sorry). In a multiplayer game you typically walk up to your "dying" teammate and apply a first aid kit or simply hold a key to slowly revive them. Thus while foreign to HeroQuest it could seem familiar to players familiar with that common game mechanic.
Thoughts on this? I suppose you could role play it further by allowing a monster to "attack" a downed hero and finish them off by rolling any skulls (since they can't defend in this state) making their death certain without any revival ability. Of course none of this accounts for what he would do with the Elixir of Life...
Of course why do death saves at all? Because player characters die and it stops them from playing and they want to keep playing! In arcade games there was the "continue" feature that let you (at the cost of additional coin) pick up where you left off or try again, which was profitable for the game owners! In HeroQuest some heroes die because they made stupid mistakes or played carelessly. Others did everything they could but went down swinging. What happens if your hero character dies for good? Another hero takes his place on the next quest (and it can still be controlled by the same person!). But many players feel the "loss" of their character and they want extra chances. Do we as GMs give it to them and if we do, how? That's up to you!