The expression “to play possum” means: to pretend; to deceive; especially, to feign sickness or death.
Early American hunters speedily learned that the opossum is a past master in the art of simulating death.
If threatened with capture it will lie with closed eyes and limp muscles, and no amount of handling or ordinary abuse will cause it to show signs of life. Only when thrown into water will it become promptly active.
That ability to show every ordinary indication of death gave rise to our expression at least two centuries ago.