If a passenger in the backseat unseatbelted is injured and the driver of the car is at fault what liability does the driver's insurance have?
When taking a one day "Driver's class" in a classroom setting, to get a speeding ticket off my record in California, the instructor told the class to read the "fine print" on your policy, because many insurance companies elect to not cover you for injury in an accident, if someone is not seatbelted. This is probably why in the Emergency Room, they always ask you multiple times, by different people, at different times, "Do you remember if your seatbelt(s) was(were) on?".
It is best to make sure you ask when shopping for insurance the question in advance, or better yet, this is why the instructor said it gives you full cause to ask everyone in the car to fasten up, before you will drive them anywhere. Otherwise, you are entitled to ask anyone who won't who will put you at risk, and everyone else in the car, to not share in the ride. (At this point, everyone will be belted in!)