If your car is stolen can the loan still continue and a new car be bought with the insurance money?

The loan on the original car was secured by the title of the vehicle. When it was stolen, your insurance company should have paid the value of the vehicle first to the lender then any remaining money should go to the owner. If the owner is "upside-down" in the vehicle he/she will be required to pay off the remainder of the note at that time or make arrangements to pay it off. No, the loan cannot be applied to another vehicle. A new loan must be negotiated.