Anything that lives that deep would need to spend most of its time conserving energy, since there's so little food at that depth. Chances are your instincts would basically be 'sit still or move slowly, unless it's time for mating or there's potential food nearby.' As far as predators go, I'd think an anglerfish would be one of the most laid back. Even hunting for them consists of just turning on the light and waiting for food to basically swim into their faces.
How the heck would one go about acquiring an anglerfish, though? Don't they die if they come into water that's too shallow? How would one morph an anglerfish without dying before reaching the proper depth?