'Scared stiff' describes their fear reaction
The most common reaction to fear is the 'fight or flight' instinct, but there's a breed of goat that just falls down.
The Myotonic Goats are a rare breed, raised at Coffee Cup Farm in Cadyville, just west of Plattsburgh. They literally get scared stiff. Owner Linda Gagnon says calcium rushes to their muscles when they get frightened, causing them to stiffen--and fall over as if fainting. She also calls them the original scape goats. "You put a couple of fainters in the livestock that you want, if the livestock gets away...the fainters become somebody's supper."