From IvanWiki

Unicorns can teleport when in danger. When they are killed, they often leave one or two valuable stones.

Eating

Black unicorn corpse:
Eating it gives you every single status in the game.

White unicorn corpse:
Eating it gets rid of any negative status you have except polymorphitis, teleportitis and confused.

Gray unicorn corpse:
Eating it will get rid of every status except teleportitis.

All will make you more chaotic.