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1. When you get so scared that you can't move at all.
2. When you get so scared that you pop a boner. This usually only happens when you are scared by an attractive member of the opposite sex.
A man jumped out from behind the brick wall and pointed a gun at my head. I couldn't run. I was scared stiff!

A hot woman in black leather boots, and with a whip in hand jumped out from behind a brick wall. I was scared stiff!!!
by The Masked and Caped Moncato July 24, 2006