If your child will no longer be regularly driving the family vehicle:
When they move off to college, talk to your insurance provider about potentially adjusting the family policy. If their school is 100 or more miles away from where you keep the family vehicle, you might be able to get a discount on your policy, since they will be driving it less frequently.

If your child is leaving their own car at home:
If they have a car with a title in their own name but plan on keeping the vehicle at home, they'll likely need to keep their insurance policy in place. When they come home to visit and drive their car, liability coverage is required. Additionally, comprehensive coverage may be required by the lender if they're still paying off the vehicle.