Can you be sued over a repossessed car?

Let me give you a brief background about car loans and lenders. When someone purchases a car and finances it by taking out a loan, until they make the last payment to the creditor (that is the the bank or finance company which lends the money), the creditor gets several important rights. One of which is the right to repossession. If a borrower "defaults" (that is they fail to make their loan payments), NY state law allows the lender to retake possession. The lender doesn't even have doesn't to go to court first. However a lender may not "breach the peace" when it is repossessing a vehicle. That means the lender must proceed with the repossession in a reasonable manner and not create a public disturbance. 

Additionally, state law provides that a lender which repossesses an automobile must give the borrower notice. If the lender repossesses the vehicle within 24 hours, it must personally notify the borrower or send the borrower a special-delivery letter informing them. The lender then sells the car at a public auction or private sale. The sale must be "commercially reasonable" and the borrower has the right to receive notice that the sale will take place

Now that's the general background; here's the answer to your specific question. If the lender sells the car for a profit, the former owner may be entitled to some proceeds (this almost never happens because auction prices are typically low). On the other hand, if the lender loses money on the resale, the lender can go after the borrower for the "deficiency". For example, if the borrower owes $12,000 on the car loan and the car is sold at auction for $10,000, the borrower would still owe $2,000 plus expenses (for such things as the cost of towing, storage, etc). In other words, the borrower is liable for the difference between the remaining loan balance and what the car was sold for (that is the deficiency), plus any cost to the lender incurred as a result of repossession. And the creditor can sue to collect (your parent's situation). If the lender wins in court it will be awarded a "deficiency judgment". It may then garnish wages, bank accounts, etc.

Note: Until the lender completes the resell, state law provides that the original borrower has the right to redeem (get back) the car. This is done by the borrower paying all of the remaining debt on the car as well as the lender's the related costs.