Many different animals and insects “play possum” by pretending to be asleep or even dead. Usually they do this in reaction to a physical threat. A spider that you capture in a cup might keel over with its legs in the air, looking as though it just dropped dead. In reality, the spider could be alive and well, but just hoping you’ll fall for the ruse and leave it alone.
Cats do something akin to this by engaging in fake sleep. This is when a feline curls into a sleeping position, closes its eyes and takes on the appearance of a sleeping kitty. It could, however, be wide-awake and only pretending to sleep. In his book Cat Body, Cat Mind: Exploring Your Cat’s Consciousness and Total Well-being, Michael W. Fox explains that such behavior often occurs at animal shelters, where cats can feel stressed out. In this case, pretending to sleep may help ward off threats, while also providing the cat with a sense of calmness.
In a home situation, hopefully the environment is calm enough that resident cats won’t feel compelled to sham-sleep. When they close their eyes, they are then likely to be enjoying true rest and relaxation.