They do so because their predators do not eat animals that are already dead and so they fool the predator into believing that they are dead.
It can be a method of self defense. I have seen dogs that thought they killed them, and they would walk away later on.
Learned
An opossum plays dead for protection against enemies
it plays dead
An opossum will do that.
Behavioural Adaptation
instinct
Opossum
Sandra Bullock plays an activist in the movie adaptation of John Grisham's novel called "A Time to Kill."
Gregory Peck played Captain Ahab in the 1956 film adaptation of "Moby Dick."
Troian Bellisario plays Spencer Hastings in the ABC adaptation of Pretty Little Liars.
Angelica Huston
Marion is played by Rebekah Staton.
We do not see Peeta's father in the movie adaptation of The Hunger Games.