Do you mean immobilized after the crash because the car was so bent out of shape? Otherwise, while a crash is actually happening, there is a LOT of movement by the driver and passengers. (even people wearing seat belts. People not wearing belts are quite literally thrown all over the car. Alway buckle up!!!)
Try taking a look at the videos on youtube from the Insurance Institute for Highway Safety. Their videos are with crash dummies (of course!), but it's a fairly good visualization of what happens in real crashes.