This is an excellent article came from the Surplus Lines Association of Illinois describing Surplus Lines insurance carriers:
In order to understand what surplus line insurance is, it is helpful first to understand a few things about the insurance marketplace and to understand what surplus line insurance is not.
The first player in the marketplace we'll discuss is the insurance company, sometimes referred to as an insurance carrier or insurer. The insurer is the company that actually writes the policy and accepts the risk that something will happen. They collect your premiums and those of other insureds and invest them. If a claim is made, they pay the claim from this pool of collected premiums.
Insurers are licensed on a state by state basis in the United States. Generally, an insurer must get a license in any state where it wants to write policies. Each state has a Department of Insurance (or similar regulatory body) that regulates these insurers. The regulation takes many forms and varies from state to state, but it can basically be divided into two general areas. First, the regulators monitor the finances and market conduct of the insurers to see that they are financially sound and using fair and honest business practices. Second, they regulate or approve the insurer's policy forms (the actual content of the policies) or the insurer's rates, or both. These insurers contribute to a state fund, called a guaranty fund, that is used to pay claims if any of these licensed insurers were to fail (go bankrupt).
The next player is the agent or broker (we'll collectively refer to them as producers). If you are an individual or company that needs insurance, the producer acts as the middleman between you and the insurer. The producer is also licensed and regulated by the state. When you tell the producer you need insurance, the producer must try to find you a policy from one of the insurers that is licensed to operate in your state. There are some cases, however, (generally less than 10% of policies nationwide) where the licensed insurers will not accept a risk because it does not meet their internally established guidelines. The risk may be too big, too unusual or substandard. In these cases, a specially licensed producer called a surplus line producer gets involved. Their special surplus line license allows them to procure a policy for you from an insurer that is not licensed in your state.
Since this insurer is not licensed in your state, they are not regulated by your state's Department of Insurance in the same way licensed insurers are regulated (they are, however, regulated in the state or country where they are domiciled or located). Since they are not strictly regulated by your state, they are generally free from the form or rate regulations imposed on licensed insurers. This gives them the freedom to maintain broader internal guidelines for accepting risks. They have more flexibility to design and price their policies and can, therefore, accept risks that licensed insurers will not.
In many states, including Illinois, the licensed surplus line producer is required to ascertain that the insurer meets certain financial standards before buying a policy from them. In many other states the Department of Insurance, or some other authority, monitors the financial condition of surplus line insurers and maintains a list of insurers that surplus line producers are allowed to use. Whether done by the surplus line producer, the state Department of Insurance, or some other entity, this financial monitoring is an important function because if the insurer were to fail (go bankrupt), there is no guaranty fund protection for you.
It is important to note that these insurers are generally not unable to obtain a license in your state, rather they choose to operate on an unlicensed, surplus line basis.
https://www.slai.org/faq/insured_06.html