An uninsured motorist can still file a claim for compensation if their economic damages were greater than the no pay, no play limits. For example, if you are in an accident and you sustain catastrophic injuries that have left you with $100,000 of bodily injury damages, you are only exempt from receiving compensation for the first $15,000 of your medical expenses. That means that if the other driver was at fault for the accident, you could still receive $85,000 worth of compensation for your injuries.