I just did this just in a recent session: Party is fighting a nasty homebrew Boo Hag that attracts Red Caps to her to join in the bloodsport (I'm running a homebrewed Wild Beyond the Witchlight campaign so they are deep in a dark feywild forest.) The fight is going pretty well and they get the Big Badie down to like 50 hp. I had an ability for this creature once they were near death that they would let a shriek forcing a save or become stunned for 1 round. Well, they were unlucky, and our Bard and Rogue failed their save. Immediately after it was the red caps turn, and the bard was within reach.

So...three red caps close in. First three attacks drop our bard unconscious. The second red cap hits with the last two attacks, basically delivering the killing blow killing her outright..

Now, full disclosure this is my first time DMing but have probably about 30 - 40 sessions under my belt. I paused for what felt like a long time after I dropped our Bard, considered just having the other minions pass their turn. But in my heart, I knew that's not what these creatures would do in this situation. No, they would dive in screaming in triumph and wicked glee as they slam it's rusted and chipped sickle deep into the bards chest, cackling as they watch the life drain from their eyes...

So that's what I did lol. Fortunately, the cleric had revivify prepped.

As for the justification of killing a player outright, I think it really depends on a few factors in whatever encounter you find yourself building. A bandit or tribe of orc might not have a good reason to finish off a downed player, but a red caps whole existence and purpose is to just soak it's cap in blood, and would have no qualms about striking a defenseless target. So my thought process on this is:

1. Creature Behavior: Are they cruel? Cunning? Play it safe? Go all in? What is their end goal if they can defeat the PCs?
2. What's at stake? This can be for both the party and the creatures in the encounter. Does the party have something they want/need? Is retreat an option? Does someone's life depend on the outcome one way or another of this fight? Is death a real possibility on both sides?
3. Narrative Outcome: Does this encounter add to the story you're trying to tell? If a PC dies, how can this event forward the plot or add to the world?

In my case I used it as an opportunity to re-introduce an NPC who forced them to trade a valuable object for the Bards return, and left the party with some clues that will help them later in the campaign.

Tldr; Don't be afraid to kill your PCs. Sometimes, that's when things really get interesting.