Final answer:
A non-admitted insurer that has been granted permission by the Department of Insurance (DOI) to cover a difficult or impossible risk is called a Surplus Lines Insurer.
Step-by-step explanation:
A non-admitted insurer that has been granted permission by the Department of Insurance (DOI) to cover a risk difficult or impossible to place with an admitted carrier is called a Surplus Lines Insurer. Surplus lines insurers are typically used when the insurance market cannot fully meet a specific risk due to high risk or unusual circumstances.