If I let someone borrow my car and they wrecked it but I only have liability, are they responsible for paying for my vehicle?

If the person, who borrowed your car, was not at fault in the accident, you can file a property damage claim with the other driver's insurance company. 

If the person, who borrowed your car, was at tault in the accident, you will need to sue that person for negligence to recover compensation for the loss of your car.  As the registered owner of the vehicle, you would be liable for the other driver's  (the party with whom your friend collided) property damage and personal injury claims and should refer the matter to your insurance company.