How is someone compensated if the other party has no insurance?

Fortunately, it does not happen often, but it may happen. The reason why it does not happen often is because most states, including Virginia, require drivers to carry uninsured motorist coverage, in addition to both bodily injury and property damage liability insurance. That means, if you’re in an accident and it’s your fault, your insurance company will pay the victim’s personal injuries and property damages up to a certain limit, and also, uninsured motorist coverage, which will pay the bills even if the at-fault driver isn’t following the law and doesn’t have insurance.
Uninsured motorist coverage means you are paying for liability coverage for yourself when the other driver does not have insurance. When that kicks in, your insurance company actually becomes the other driver’s insurance company and stands behind them and will cover your personal injury claim as if they had insurance, up to the policy limits of your uninsured motorist coverage. That is to protect each of us from the irresponsibility of people who drive without insurance.
That is how you’re compensated when the other person has no liability insurance coverage on their motor vehicle. As a result, in about 99.9% of automobile cases, there is coverage for personal injuries incurred and personal injury claims, from either the other person’s liability policy or from your own uninsured motorist coverage taking care of you when the other person doesn’t have insurance.