Alaska has both Mandatory Insurance and Financial Responsibility laws. The Alaska Department of Administration's Division of Motor Vehicles notes that the purpose of these laws is to ensure that drivers and owners of vehicles using the streets and highways are financially responsible for any damage or injury caused by motor vehicle collisions and to remove financially irresponsible drivers from the highways.
The mandatory insurance law requires the operator or owner of a motor vehicle subject to registration to have motor vehicle liability insurance in effect when the vehicle is driven on a highway, vehicular way or area, or other public property in the state. The owner's or driver's motor vehicle liability insurance policy must meet the minimum coverage amounts required by law.
The minimum coverage amounts in Alaska include bodily injury liability in the amount of $50,000.00 for injuries or death to any one person, $100,000.00 for total injuries or death per collision. Also required is $25,000.00 for property damages.
The Mandatory Insurance Statutes which require that the owner of a motor vehicle subject to registration to have a liability insurance policy in effect can be found by reading Alaska Statute (AS) 28.22.101.
The Division of Motor Vehicles must suspend the driver's license, privilege to drive or privilege to obtain a license of drivers who fail to provide proof of liability insurance. The suspension period can be 90 days to 1 year depending on prior license actions. If the motorist is in an accident, the license suspension will occur even if the driver is not at fault in the collision. Your vehicle may be impounded in the Municipality of Anchorage if you do not have proof of insurance.
As for federal repercussions for your Russian friend with a student visa you may need to contact US Customs and Border Patrol (CBP) or U.S. Department of Homeland Security to get information.
What we did find out is that the CBP does strongly advises those with visas that leave and return to the US to pay their traffic tickets and abide by state laws. Unpaid tickets or other issues with a state DMV would not subject a person to arrest when coming back into the US, unless a warrant is issued, but the person may be subject to a more intensive inspection if their record is not clear.
Your friend can get an auto insurance quote for Alaska here with us so that she is driving legally in AK.