Just clarifying a point that is obvious to people who work with insurance companies but may not be quite so obvious to people who don't. No shame to them - no one can be expected to know everything. But confusion on this point sometimes leads to misplaced expectations.
An insurance company cannot be required to (and will not) pay out more than the limits of the policy. Just throwing out numbers here - if the limits of the policy are $25,000 and you sue the driver and are awarded $50,000, the insurance company will send you a check for $25,000 and you'll have to go after the driver for the rest.

