To feign death; to remain quiet and still to escape attention or remain undetected; to lie low.
The soldier played possum, fooling the sniper.
To feign sleep, illness, etc.
When we used to get home late at night, I would play possum so my daddy would carry me inside and put me in bed.
To dissemble or to feign ignorance; to disguise or conceal something in order to deceive.