Normally the plaintiff will settle for the amount of the insurance. However, I have known of cases where the family was sued personally and lost a significant amount of money. That is one reason I always advise carrying enough insurance to protect your assets, especially if there are teenage drivers in the family. An umbrella policy is normally very cheap coverage.
One option would be to file bankruptcy depending on the circumstances. Each state has a "homestead" that cannot be touched either by a judgment or bankruptcy. If the other party does get a judgment in excess of the insurance, they can collect in accordance with the laws of your state. They can garnish your wages or bank account and place a lien against any real estate.
If the overage amount may be large, you should with your own attorney and not completely rely on the attorney furnished by your insurance company.
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