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Does the primary lease holder on a car lease have any liability if the car is in an accident if the car is registered and insured by the co-signers of the lease who is not the primary?

If others who are co-signed on the car are in an accident, and cannot afford to pay and charges or fees as a result of that accident, then yes, as a co-signer the primary lease holder will be liable for those oustanding payments.

What if You are in a car accident and have no insurance and you hit a car that had utter coverage and gap insurance what will happen?

Generally, if you were in CA and I am assuming you are not talking about a fender bender or minor accident, you would lose your license and be required to make a filing to reinstate your license.