Rear-ended in a car accident

If you are rear-ended in a car accident, is there a minimum legal compensation that is allowed in a lawsuit as an injury claim?

There will be a basic list of what they will claim for as far as injuries are concerened. But you have to remember that some people take time to recover and incur fees for physio. The claim will close when all parties reach agreement and may include interim payments if required. If you were rearended then they will pay up to the book price to have your car repaired. If it will cost more you will get book price of your car, It is up to you pay off any loan you had on the car before you use the balance towards another car

With a rear end accident, no dispute of fault. 

But any injury settlement is based on (where) you live and the laws of your state. 

Settlements are based on your injury only. If whiplash, then maybe owed "something", but if scarring, disfigument, surgery, loss of a limb or a permanent injury or impairment could be a lot. 

But, any settlement no matter how bad or not, insurance can only pay the limits of the policy, so if you have medical bills of $50,000 and they bought only $10,000, then you can only get $10,000 and still owe $40,000 in medical bills.

The first thing to maintain is the tires and making sure to rotate them and keeping them properly inflated. With properly inflated tires, your car will get better gas mileage and handle better on the roads. Tires leak naturally, so they need to be checked regularly. Over or underinflated tires will wear out more quickly. To ensure equal wear on the tires, they should be rotated on a schedule that is recommended in the manual. Sometimes people will not think about their windshield wipers and the need to replace them. Good wipers can prevent an accident and worn out ones can hinder visibility.

I don't think so. Your lawyer is gonna try to find some somewhere. 
You have to hire an accident lawyer for this. (yes they take the first60% IF THEY WIN) and they DO try because they have an incentive. Losing=nothing) It comes out of the insurance companies (theirs and yours) Some drivers do not have insurance(pray you do not have that situation)because no insurance means you have to sue the other driver(if he has nothing, then you are trying to get Blood from a stone.)