There is a very similar question here, but it is asked and answered using 4e rules.
In 5e, Elementals all have the Condition Immunity to the Unconscious condition. We have been playing it that it confers immunity to spells and effects that would confer unconsciousness without necessarily affecting HP, such as the Sleep spell. I can't find a reference as to what happens when the Elemental drops to 0 HP through combat.
Most DMs follow the recommendation of the DMG and just have the creature die, since it is a monster. However, characters are given the option of knocking a creature out rather than killing it at 0 hp. And some DMs do indeed allow important monsters death saves.
What happens when a creature with this immunity drops to 0 HP? They cannot go unconscious. Are they incapacitated? Can they act?