The relevant rule on monsters and death saving throws says:
Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws.
Mighty villains and special nonplayer characters are common exceptions; the DM might have them fall unconscious and follow the same rules as player characters.
So I suppose we would expect that, if an NPC were special enough to have a magic item, the DM would probably consider that NPC to be special enough to get death saves.
A different way to think of this: it's not that random monsters shouldn't get death saves, it's just that it's too much work for the DM to roll them, so most DMs will just call them dead to avoid bookkeeping. If a monster is wearing a periapt of wound closure, the DM would likely call them unconscious-but-stable to avoid bookkeeping.
In my own games, I assume defeated opponents are dead, unless one of the PCs expresses an interest in keeping them alive for interrogation, in which case I go back and roll the death saves to see if they're alive. That seems to work fine.
Ultimately it's up to the DM, though.