Generally speaking (and I don't know the statute of limitations or repossession law of KY; it could offer you some protections), the answer is "Yes." Loan companies are, in most cases, allowed to collect any balance remaining after repossession (including fees, costs, advertising, auctioneer, etc.) at any time before the applicable statute of limitations expires.
I recommend that you check with a local consumer protection or bankruptcy attorney, who can best advise you about your options.
Under the Uniform Commercial Code, which is followed in most states (and I presume it is followed in Ky), after repossession, the creditor has the right to sell the collateral (the car) in a "commercially reasonable manner" (Which is typically at a recognized auto auction, but may be at a private car lot) after providing notice to you. Then the creditor can take the proceeds of the sale, deduct the costs of the sale, and then apply whatever is left to the unpaid debt. If there is still money owed, then the debtor (you) sill owes the "deficiency balance."
From the creditor's point of view, the creditor doesn't want your car. The creditor loaned money, and is entitled to get that money back. The car is nothing more than an asset making sure that the creditor can recover some of its money by selling the collateral. However, most people with car loans are "upside down" on the loan, and thus owe more on the car than it is worth. You are caught in the standard trap that anyone who buys a car gets trapped in unless he or she puts down a large down payment.
There are some technical defenses that may be asserted if the creditor made some mistakes. I suggest you speak to an attorney who handles "consumer legal matters" in your area.
The short, and quick, answers to your two questions (from a Kentucky lawyer) are "yes" and "yes."
There may be some defenses, as one of my colleagues suggests, but to analyze that would require more information than is available here.