1
general::
Pretend to be dead or asleep, as in Max always plays possum when it's time to clean up his room. This expression alludes to the fact that the opossum falls into an apparent coma when caught, giving the appearance of death. [1820s]
American Heritage Idioms
2
general::
Phrase(s): play possum
Fig. to pretend to be inactive, unobservant, asleep, or dead. (The possum refers to an opossum.) • I knew that Bob wasn’t asleep. He was just playing possum. • I can’t tell if this animal is dead or just playing possum.
McGrawhill's American Idioms And Phrasal Verbs