Playing dead was the act of feigning death (people and animals) or destruction (starships) to avoid being attacked or to lure the enemy closer.
It was a common tactic employed in zombie movies. In 2259, a USS Enterprise away team sneaked a shuttle past Gorn forces by playing dead. SNW: "Hegemony")
In 2266, Captain James T. Kirk suggested the USS Enterprise play dead to draw a Romulan ship out. (TOS: "Balance of Terror")
In 2370, a Ferengi ship was playing dead until the USS Enterprise-D approached it. (TNG: "Force of Nature")
Opossums were known for playing dead (SNW: "Memento Mori") which gave rise to the synonymous term "playing possum". In 2377, Kathryn Janeway rejected Chakotay's suggestion that a damaged Hirogen ship was a trap for USS Voyager, stating that "The Hirogen aren't the type to play possum". (VOY: "Flesh and Blood")