You look where you're going to end up, so if you stare at the ground..... Of course you're going to end up there.
I would spend a lot of time with this rider on the lunge line stabilizing her seat and developing a feel for what is going on underneath her before I'd send her over jumps. Jumping over cavs on the lunge line might also be a useful exercise down the road. It is obvious she has lost confidence in her riding and needs to be taught how to effectively stabilize her weight in her lower body and seat.
Wearing proper riding attire will also help this rider to be more secure in her riding. This includes breeches, halfchaps and a pair of gloves.
The gloves are important because right now she is not holding onto the reins and as a result is not able to effectively steer the horse, or use her closed fists on the side of the neck to support her body weight. The hands must be closed on the reins at all times to allow the development of a correct contact - imagine having a phone conversation with someone standing 10 feet away from their phone. You and they have to yell to hear each other and then all of a sudden that person runs to the phone and keeps talking at the same volume (ie when you pick up contact to go over a fence) and of you're going to recoil (refuse the fence).
Anyways, lunge lessons and correct attire are my suggestions.
Good luck to your friend!
ETA that fleece thing needs to be burned. It is really affecting her position badly and not giving her a place to sit and feel the horse. You can send it to me. I like burning things