RPGMemes

Some games have this built in and you don't have to fudge it.

Fate, my go to example, has important but simple rules around losing a conflict.

At any point before someone tries to take you out, you can concede. That's a player action and not a character action. If you concede, you get a say in what happens to your character. That's where you as a group say "maybe they stab me but leave me for dead in the confusion" or "maybe the orcs take me prisoner so you all can rescue me next week". Whatever the group decides is cool goes, but you get a say. You make this call before the dice are rolled. You also get one or more fate points, which is nice.

If you instead push your luck and let them roll, and their attack is more than you can take, you're done. The rest of the table decides what happens but you don't get a say beyond what was agreed to in session 0.

This would also be pretty easy to import into DND or most other systems.

That's why revivify is for. What you did here is taken away a meaningful moment from a player, just because you wanted them not to make a different PC. If you want that moment, write it into the story with an NPC. Don't keep someone alive "just because". Playing "hardcore" has nothing to do with this - that's about balancing enemy encounters. Don't throw a dragon at an unprepared party sort of things.

Otherwise people will either be annoyed that a moment was taken away, come to the conclusion that their choices don't really matter, or they would expect of you that every time a character dies, they become "half concious". Suddenly you have a "why didn't my char do that???" moment at the table. It's the same with fudging dice, but when that happens, you are behind a GM screen so you are less likely to be found out. Still a shitty thing to do though.