As I mentioned earlier, you will want to review the finance company's internal controls. For example, you will want to know what its policy is for inspecting the inventory, if that policy is actually followed, if the finance company's inspectors are rotated, and what the car dealers' history of paying out of trust is. In other words, did they sell cars and not make the appropriate payment to the finance company?
I'm guessing that these aren't dealers of new cars, otherwise they would have floor plan arrangements through the manufacturers' captive finance companies. If they are dealing in used cars, you'll want to look at the finance company's policy regarding inventory turnover, particularly for cars that have been on the lot over X days. After that time, there should be a so-called curtailment payment policy that requires the dealers to begin paying down on the stale inventory. This gives incentive to the dealers to move the cars, either through retail sales or auctions, to keep a fresh inventory.
Those controls along with verifying the veracity of the finance company's financial records and legal standing, and ferreting out any pending litigation would seem to me to be the most important parts of your due diligence.
If these are new car dealers, you will want to know why they don't use the captive finance companies. I would view this as a red flag that may be an indicator of the dealer's financial condition, thus making the finance company a riskier proposition for your bank.
One final thing. If you are going to be a lender to dealers, I'd check their waste management practices, particularly if they have service or repair shops. There's nothing like an action from the EPA to stand in the way of getting repaid. AR.