In the high chaos version of this mission, you have to either kill or neutralize Havelock, despite only being an optional objective. In high chaos, at the final confrontation with Havelock and Emily, if possession is used on Havelock and he is walked down to the lower platform, he will fall unconscious once it ends.
What happens if you kill Admiral Havelock?
If Corvo kills Havelock with a ranged attack or power, Havelock will fall, but Emily will grab the edge of the platform. Corvo can then pull her up, but if he takes too long then Emily will fall to her death. It is also possible to deal with Havelock non-lethally in the High Chaos ending.
How do you get the good ending in Dishonored?
Dishonored has two different endings depending on how you play the game. If you kill everyone you will get the evil ending (high chaos ending). If you don't kill very many people, you will get the good ending (low chaos ending): At the good ending you'll save Empress Emily Kaldwin.