The driver of the car who runs a stop sign is at fault, there's just no question about that. Even though they are clearly at fault, the victim's insurance company will pay the first $10,000 of their medical bills under Florida's No Fault.
But the driver who caused the accident is responsible for everything else. This includes medical bills that PIP did not pay, future medical requirements, pain and suffering, and the loss of the ability to enjoy life, what makes life special to the person who got hurt. All of these consequences, the harm that was caused by the driver will be the responsibility of their insurance company after this type of an accident.