Most states allow you to self-insure by depositing a specific amount with your Department of Motor Vehicles or your state's insurance department. If you have an accident, the deposit you have made can be used to pay for the damages, injuries, and related claims against you, but that is not how it is meant to work. Think of the money as a security deposit that will only be used if you do not pay the accident costs in a timely manner.
The money you deposit with the DMV is a type of surety bond, not your actual insurance coverage. The purpose of the deposit is to illustrate that you are prepared to pay for any claims filed against you. When such a claim is filed, you are actually expected to pay for the claim out of pocket, not subtract the amount from your bond deposit. For all intents, the deposit is simply a way of stating that you are financially able to pay for your own at-fault costs.
You should be aware of the fact that an actual insurance policy will offer you much better protection. For example, if you are at fault in an accident and the injured party sues, you will have to pay for the cost of litigation as well as any judgments against you. With an insurance policy, legal representation is included in your liability coverage. Self-insurance may be an option, but it is far from being the equivalent of an insurance policy.
If you are required to carry an SR-22 Certificate of Financial Responsibility, you may not be eligible for self insurance. If you are, the amount of your deposit will be much higher than the mandatory minimum. In some states, self insurance is only available to businesses, and may even be limited to companies with a minimum number of vehicles, usually 10 or more.