If you were involved in an accident with a driver whose insurance is insufficient to pay for the damages incurred, you'd probably need to rely on your own insurance to cover your losses. For most people, this would be covered by underinsured motorist (UIM) coverage, which is usually add-on protection from your insurance company. UIM coverage is only required in a few states, although insurance companies are required by law in most states to offer it to customers.
If you live in a no-fault car insurance state, your own insurance will be paying for your medical bills and other damages after the accident regardless. Therefore, the fact that the at-fault party doesn't have enough insurance matters much less. Consequently, filing a lawsuit against the at-fault driver is more complicated and only relevant in a handful of scenarios. If you're considering filing a lawsuit, speak to a car accident lawyer to learn more about whether you live in a no-fault state and what can be done about it.