An insurer only has to pay up to the policy limit--they are not obligated to pay any more than the maximum amount in the policy for these circumstances. If you were injured by another, at-fault driver (you can only sue an at-fault driver) and the amount of your medical costs, property (e.g. car) damages, lost or reduced wages, "pain and suffering," etc. exceeds the insurance limit: you can sue that other driver (not the insurer) for the additional money, provided you did not sign anything (e.g. a settlement or release) in which you contactually gave up your right to sue or agreed to not sue.