To act possum

from The Collaborative International Dictionary of English v.0.48

Possum \Pos"sum\, n. [Shortened from opossum.] (Zool.)
   An opossum. [Colloq. U. S.]
   [1913 Webster]

   {To play possum}, {To act possum}, to feign ignorance,
      indifference or inattention, with the intent to deceive;
      to dissemble; -- in allusion to the habit of the opossum,
      which feigns death when attacked or alarmed.
      [1913 Webster]