I wanted to add a dead elk to a pack of wolves (their kill), but the creature I made stands up dead. It doesn't lie down, or settle or anytrhing, just hangs there dead.
Double click the reference and check 'Starts Dead'. Then, no matter what it will start out dead. Once checked, you can then also place it by enabling havok.
Select "starts dead" for your creature. Then activate Havok sim (alt-H) to simulate the fall. After that, you can place the body with ALT drag to move some parts.