When renting a car from a major car rental company, what liabilies or
other penalties might be risked when individuals drive the car without
being registered as named drivers with the rental company? Assume that
these unnamed drivers have their own comprehensive car insurance,
which covers them to drive other cars.

I would question whether the unnamed driver's insurance covered him
when he was driving a vehicle in breach of a rental contract.  The
rental company would probably first hold the party to the rental
contract responsible  - within the terms of the rental contract, and
the actual driver's policy would claim that it did not cover a risk
for which another party was held responsible.

But I am no expert, and this is no professional or legal advice, and
this comment is not an answer to your question.

Myoarin

I believe they get you on a technicality -- If you are not on the
contract, then you are not authorized to drive the vehicle.  If you
are not authorized to drive the vehicle, then it is effectively no
different than you stealing the vehicle.

As such, I don't believe the unlisted driver's insurance will do
anything except for saying "tough luck". Likewise, the insurance of
the person who is on the contract will probably say "well, they
weren't authorized to drive the car, so tough luck"

It's best to go by the rules and list the other person on the contract...

On a messageboard that I visit, there was a recent post about a sad
case in which a person allowed his friend to drive a rental car, even
though the friend was not listed on the contract as an authorized
driver. The friend totalled the vehicle, and the insurance companies
of both the car renter and the driver rejected the claim, leaving the
car renter liable for the replacement value of the car, approximately
$20,000.