Did the seat belt fail?
From your description, the seat belt worked perfectly and entirely as designed. Her injuries are, thankfully, limited to some severe bruising across her abdomen and shoulder, and pain that she describes as muscle soreness. This is the result (on the person) of the seat belt doing its job of slowing down a large amount of mass (a person) from a very high energy collision (45mph is FAST in crash terms). the seat belt was fully extended and hanging loosely, and the buckle had come undone. The seat belt did not retract after the accident, and appears to have not locked during. This is the result (on the belt) of the seat belt doing its job. Belts stretch – they are designed to do so. They also lock with an inertia based system, not permanently, so it will not remain locked after the initial accident but may no longer retract due to the stretching. Seat belts are a consumable item,in a crash situation and should be replaced after every decent sized impact as they deform to do their job prop