if it was shut down by BLP, it has to fall according to the hit direction.
if it was "killed" by laser/plasma/MF, then it has to fall according to the slope it was standing on, or towards its movement direction (if it was not standing still), or randomly if it was standing and there was no slope at all.
if it was taken down by melee, it better break down in half and the pieces should fall with respect to the power of the cutting blow + gravity.
if it was blown in pieces by rocket/grenade, it must not be visible falling any direction in one piece.
Since the drone mimics the human body, it falls forward. Without any force exerted on the body, such as from a weapon, the human body tends to fall forward in unconsciousness to protect the back of the head. In most combat though, it would be more realistic to fall backward.