You are right the dealer has messed up on this from a business practice perspective, but that is not related to a legal perspective. Most times the dealer will tell the customer to call the insurance company right there or you can go online add the car, and are covered once the insurance company accepts, usually in a minute. I will assume she did not have collision on the trade in, if so then that would cover a purchased car, most insurance companies cover the car at purchase and give you X days to report to them the purchase. Does the contract have VSI, read the contract, that covers the loan amount if car is totaled with no insurance. Probably does not.
7550 - 2500 down = 5050. That is what she owes.
As for the contract those are either two party or three party. Very important, read your copy of the contract. A two party is buyer - lender, three party is buyer to dealer to assignee (lender). But the dealer may have another piece of paper work that states deal is contingent on financing. It does happen where dealer cuts a corner or messes up, bank rejects contract and dealer has to call customer to bring back car. Usually in those cases the title has not been transferred so customer can protest, but they are driving a car they don't own and dealer can go get it (not repo) as the dealer is the owner. And the customer can't get plates after the temp tags expire.
Could they sue or try to report her credit if they hold a valid contract, sure. Would they win, I don't know, they would be considered partially negligent and assuming the risk by letter her drive without insurance.
Write up what happened and hire an attorney, not talk to, hire them to deal with situation. You might have zero liability. It is the details of the contract and your state law, maybe they broke the law by not verifying insurance? Who knows. My concern is her credit, the 2500 is not easy to swallow, but credit scores are used by insurance companies, ie lower score higher rates and employers use credit scores in hiring decisions.
And if you settle the matter you will need a documented settlement, TRUST ME the dealer will take your money and then if you don't have the right documentation they will try to collect the rest. And how do you deal with the value of the totaled car, and the sales taxes, they should try to get that reversed, and any other fees they charged.
They are the experts.
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