In Massachusetts the compulsory motor vehicle liability insurance law requires that all cars have insurance on them with the minimum limits of $20,000/$40,000 for bodily injury and $5000 for property damage. From this wording it would appear that it is the vehicle and not driver that the insurance must be on to comply with the law.

If this is the case then a person with a valid MA driver's license but does not own a car to put insurance on, and does not carry a non-owner's policy, should be able to drive other people's insured cars with their consent. The person giving the uninsured driver permission to operate their vehicle should check with their insurance provider though to make sure the friend they are lending the car to will be covered by the owner's policy if they are in an accident. 

If the person is going to borrow their friend's car on a regular basis then the insurance company may require that person to be added to the policy in order for them to be properly covered.