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A little more information is needed.
If killing them is a game over or full health recharge, they're a Puzzle Boss where the puzzle is getting them to near health-depletion without being too high or too low.
If it's because they flee rather than risk actual defeat, see Villain: Exit, Stage Left or Screw This, I'm Outta Here.
If they really should have died from that nuke to the face, but kept a sliver of health anyway, that's Gameplay and Story Segregation.
Let's also keep in mind that Hit Points in many games do not necessarily indicate actual injury nor a linear progress toward death. It's very common for hit points to be time until defeat or incapacitation anyway.
Absent any of these other considerations, it just seems like a tiny distinction to say you win when the boss reaches 1 health rather than 0 health. It's a misleading Life Meter, which could be a thing, but it's misleading to the player's benefit. That's like 1 health point you don't have to deal with.
There's also Coup de Grâce Cutscene, for when the boss is finished off outside of gameplay.
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A boss fight ends not you when kill them, but when you ALMOST kill them