I've currently read this question about the so-called My Guy syndrome, and since I recently started DM-ing myself, I couldn't help but wonder - is there an equivalent of this for a DM?
A short summary of the syndrome as I understand it:
My Guy syndrome is when you make your character do something, just because you believe that it's what your character - your guy - would do, despite the fact that taking that course of action would upset everyone (OOC), ruin the fun in playing the game and be highly detrimental to the atmosphere.
Now, if you are the DM, you don't have your guy, but you have lots of guys, and one of those guys (particularly monstrous ones) might one day happen to be in a situation where that guy would kill a player (not knock him unconscious), even though there are other party members nearby.
I don't have a specific example right now (feel free to edit and add one), but it could be, for example, something along the lines of a fiend that draws particular power from obtaining a creature's soul.
The particular situation doesn't matter, just assume that the creature, lore-wise, would prefer to finally kill an unconscious, near-dead character as opposed to knocking out another, non-unconscious one (I'm using D&D 5e terms here, but just replace "unconscious" with whatever would be near-death in your system - maybe simply low hit points).
So, to my actual question: Have you experienced this situation as a DM, and if so, how did your players react to you killing the player? Or if you decided against killing the player, was there any particular reaction, aside from a to-be-expected sigh of relief?
Please differentiate depending on whether or not the party has access to means of reviving a dead character.