In some cases, if a family member is visiting and has permission from the insured to drive the family vehicle, there will be coverage if there is an accident, but the coverage may be limited. All policies should be reviewed to determine if there are any excluded drivers and any limitations on coverage for anyone driving the car that is not specifically named on the policy.
There are certainly insurance carriers and policies that will not cover any driver not specifically named in the policy. Other relevant facts include where the “other driver” resides and if they are related to the insured. In general, if someone is living in the insured’s household and regularly drives the insured’s vehicle, many insurance carriers expect you to have that person named on the policy. They will need to undergo the same underwriting and qualification process as any other policyholder.
But liability coverage levels come in threes — you’ll probably see something like 50/100/50 up to 250/500/250 in typical policies. You can think of these limits like: individual injuries / total injuries / property damage. Insurers are a little more technical, calling them bodily injury liability, total bodily injury liability and physical damage liability.