I'm not sure that's really a fight or flight response since passing out would leave one extremely vulnerable to harm from predators, the environment.
I have a friend who's girlfriend was driving one day and the car slipped off the road going towards an electrical pillar (it didn't hit it though because my friend managed to grab the wheel). Near the collision point with that pillar his girlfriend passed out, in an instant. We laughed at that situation for years. They ended up in someone's yard, killing a poor dog in his little house.