Can't squeeze blood out of a turnip. If they go to trial and the jury awards in excess of your policy limits, that's the problem of your insurance company, not you.
Au contraire, mon amie.
If the jury awards damages in excess of the policy limits, the excess becomes the liability of the defendant.
It just doesn't go away, either.
And, if the plaintiff is persistent, it can hamper the defendant forever.
Most plaintiffs don't bother going after it, nevertheless they have that judgment.
But, some place a lien against property, garnish wages, or seize assets.
I know one plaintiff that received such a judgment more than 30 years ago.
Every 10 years he gets it renewed.
In some states, unsatisfied judgments from motor vehicle accidents can cause you to lose your driving privileges.
Those unsatisfied judgments can also require you to seek SR22 filings.
This is what Texas requires in situations where the judgment is unsatisfied.
2) Liability Judgment. When the Texas Department of Public Safety (DPS) receives a certified copy of an unsatisfied judgment arising out of a traffic crash that occurred on a public street or highway, the person(s) who the judgment is rendered against is subject to suspension. Texas Transportation Code 601.332, 37 Texas Administrative Code 25.03.
Reinstatement requirements
* Comply using one of the following methods:
Provide evidence that the judgment has been satisfied in the form of a Release (form SR-11); or
Court Approved Installment Agreement (If DPS receives notice that a driver has defaulted on the court approved installment agreement, the license is subject to suspension); or
Judgment Creditor's Consent Form (SR-84). And submit an SR-22 certificate of insurance if within 2 years from the date the judgment was rendered.
If a suspension has been enforced, a reinstatement fee will be required prior to the renewal/issuance of a driver license.
Note: If the judgment is over 10 years old you may file a certificate from the court in which the judgment was rendered that a judgment has not been renewed. Submit the required reinstatement fee.
http://www.txdps.state.tx.us/administration/driver_licensing_control/faq/answers_sus.htm