To be extremely frightened; panicstricken. The earliest version of such hyperbolic expressions seems to have been to be scared or frightened
out of one’s wits, which appeared in print in 1697: “Distracted and frighted out of his wits” (Bishop Simon Patrick,
Commentary). Later it was frightened or scared
out of one’s seven senses (used by Jonathan Swift and Sir Walter Scott), still later replaced by
silly, with the same meaning.
Stiff alludes to paralysis by fright,
death to dying of terror. A mid-twentieth-century equivalent is
to scare the pants off someone (Ogden Nash, and others). Also see
shake in one's shoes.