If the car had a hail loss paid on it, and the vehicle was considered a total loss....in Kentucky it can have a "Hail Damage" title. This automatically happens as part of the claim process. The insurer either takes possession and sells it for salvage, or "sells" it back to the owner with the modified title. This title indicates that there is cosmetic damage that resulted in repairs exceeding 75% of the value of the vehicle, but it is otherwise it is fit for legal operation on the highway. (My son's car meets these definitions, we essentially came out ahead on the deal.)
Insurers will still insure the vehicle, for liability only. They won't cover physical damage coverage on them though. So, yes, financing through standard means could be difficult, as the loan couldn't be secured through the value of the vehicle without an insurer willing to insure it. That means higher rate unsecured loans.