There is some variance when it comes to specific details by generally yes they can as long as the parent maintains ownership interest in the automobile that is covered under the policy.
The parent should be well advised of the fact that claims experience does effect rates with most carriers and as such claims made by adult children--even if they are no longer included in a parent's policy--can affect future premiums for the parent.
Enrolled Agent-licensed to practice before the IRS, Samuel N Smith, EA, South Carolina
Generally married children cannot be on the parents policy. What happens if you try to hide this "material fact" and you have an accident and now you need to file a claim? Usually if you are on your "parents" policy the parent is the "primary" driver and you are a child that just drives your parents car sporadically. If you or your spouse have a vehicle and you have the car financed in your name and your parents are not on the note-can you say Red Flag?
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The parent should be well advised of the fact that claims experience does effect rates with most carriers and as such claims made by adult children--even if they are no longer included in a parent's policy--can affect future premiums for the parent.