For The Knock-Out

Consider: defeating a foe without killing them. Knocking, as it were, them out.

3.5e

In 3.5e, all damage was lethal, unless you had a weapon that specifically did nonlethal damage (such as a sap, a whip, a Merciful magic weapon, or your fists) or you took a small penalty to do nonlethal (such as striking with the flat of your blade, the butt of your spear, that sort of deal). Some creatures (such as, IIRC, undead) were immune to nonlethal damage.

Nonlethal damage was handled in a way that was presented somewhat complicatedly but in fact was pretty straightforward.

Technically, it's a separate pool of damage, and you add your nonlethal damage taken to your lethal damage taken: if your lethal damage is greater than your maxHP but not enough to kill you, and your lethal+nonlethal damage is greater than your maxHP, then you are unconscious instead of bleeding out / dying. And then there were some more fiddly rules about, like, taking so much nonlethal damage that you die anyway.

In practice, all of that wound up resulting in something more like: if you take enough total damage to bring you below 0, and any of it is non-lethal, then you are unconscious instead of bleeding out / dying. End of.

5.5e

In 5.5e, all damage is undefined vis-à-vis lethality until the strike that brings an enemy to 0hp, at which point: if a PC is doing damage in melee to an NPC, the player decides whether it is a killing or KOing blow. Melee spells, and certain weapons, are up to DM adjudication whether they can be nonlethal. Otherwise, the enemy dies.

I house-rule to broaden this slightly from RAW: if a PC defeats a non-major-NPC foe by any kind of damage, the player decides whether it's a killing or KOing blow, with the specific line where DM says to player: "describe the manner of the foe's defeat". (Major NPCs work by PC rules: making death saving throws when unconscious.)

The logic here is reasonably strong: let the PCs advance the story however they seek to: by taking prisoners, if they seek to interrogate mooks, or to not feel bad about too much killing, or whatever.

An issue arises: if they seek to interrogate and acquire information faster than the DM wants to dole it out. Which isn't a problem, per se -- the PCs should be able to do that if they want! The problem, if there is one, is this: the PCs can accomplish this thing with no special effort. Which, again, might not be a problem -- they went to the effort of defeating the foe, after all, so there is of course still effort involved, just not special effort.

The baseline 5.5e rule requires at least a little bit of forethought: prepare incapacitating spells like sleep instead of just fireball, whack with a sword instead of shoot with a bow, etc. So if there is a problem, I'm causing it myself by loosening the restrictions on nonlethal defeat. Just don't be so permissive; problem solved. Ish.

Let's Contemplate Alternatives

But, if I do want people to be able to pin the foe to the wall with arrows; modulate the temperature on their fireball to scald to cause passing-out instead of kill; I don't know, that general kind of thing, not permitted by RAW?

My instinct is to go back to something 3.5e-esque but simpler: all damage is lethal by default; you can designate any attack as nonkilling by taking Disadvantage (or giving the foe Advantage on their save); if such a hit lands, then: if it defeats the target, then the target is unconscious; if such a hit does not defeat the target, then it's regular damage.

This ameliorates 3.5e's slight weirdness where, if any damage you've taken has been nonlethal, then you pass out instead of dying when you suffer critical existence failure at 0hp.

However, it is much harsher than the permissive take where any defeating hit can be retroactively(ish) nonkilling once it hits and defeats, and a bit harsher than 5.5e's RAW where if you can retro-decide a blow is nonlethal iff that hit is with a melee weapon.

Perhaps my revised take should be a combination: iff you hit in melee, you can decide at time of damage whether it is a killing or KOing blow (as in 5.5e by RAW); otherwise (if you attack at range, with a spell, or any other uncertain situation subject to DM adjudication), you can take Disadvantage (or give the enemy Advantage on their save) to give the attack the option to be nonlethal.

You could even make the Disadvantage retroactive (for just the expanded-from-RAW situation (if you want to be slightly more permissive than RAW) or for every kind of attack (if you want to be slightly less permissive than RAW)): you attack regular-like; you hit; it is revealed that the damage would defeat the foe; then you are given the choice: either you kill the foe dead, or you reroll your tohit (or the foe rerolls, if they failed a save).

...actually, I think I kind of like that.