Yes.
If you find yourself in a situation where the liability insurance proceeds are insufficient to pay for all of your medical bills and pain and suffering, then you still have a claim against the at fault driver. However, before you file a lawsuit, you have to determine whether the at-fault driver has any assets that will be available to pay for your medical expenses and pain and suffering.
To start learning about the assets of the at-fault driver, talk with your own Underinsured Motorist Coverage insurance carrier, and see if they have done an asset search. Also, you can do your own asset search by searching the at-fault driver’s name through your local county register of deeds (looking for real estate) and your local county tax assessor office (looking for personal property and real estate).
Even though you can sue the at-fault driver in this type of situation, it is relatively rare to do so, as, unfortunately, many people who carry very low liability limits also often have very few (and often no) collectible assets. It kind of makes sense, as one of the purposes of purchasing liability insurance is to protect your personal assets, so if you are purchasing the absolute minimum in liability limits it tends to signal that maybe you are not all that concerned about being sued (perhaps because you do not have any money or assets to pay someone).
The most common scenario where there is additional money or assets to be obtained to pay your medical bills or pain and suffering is where the person who is at fault for your injuries is an employee of a business (where you may be able to hold the business liable for the actions of its employee).
If you have questions about whether it makes financial sense to pursue a lawsuit against the at-fault driver for money in excess of their liability insurance limits, be sure to not sign a release and speak with a Durham personal injury lawyer.