I hope your niece is Okay.... Bravo for getting the gap insurance. I always recommend it especially during the first few years of your car loan since this is the time when you are most likely "upside down" on the car. The insurance company will evaluate the car. Then, if the insurance company's evaluation is less than the loan balance, the gap insurance will cover the difference. The only way your niece will net any money is if the adjuster's evaluation is more than the loan balance. Be sure to notify the gap insurance company of the accident so that they will be ready in case a "gap" claim needs to be made.
Another option is to push the claim through on your own insurance policy. They might come up with a better evaluation (even after the deductible) than the truck's insurance company.
Hopefully she was not seriously injured. Great advice from Attorney Slim. GAP insurance is made for this very situation. Depending on your niece’s policy, she could get full replacement value for her car since it is only a month old. She needs to talk with her insurance agent ASAP to see what her policy specifically covers.
DISCLAIMER: David J. McCormick is licensed to practice law in the State of Wisconsin and this answer is being provided for informational purposes only because the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship.
The two attorneys who have already answered have provided sound advice.
This email (including attachments) is covered by the Electronic Communications Privacy Act, 18 U.S.C. §§2510-2521 and is confidential. If you are not the intended recipient, you are hereby notified that any retention, dissemination, distribution, or copying of this communication is strictly prohibited. This email (including attachments) is intended for the use of the individual or entity to which it is addressed and may contain information that is privileged, confidential and exempt from disclosure under applicable law. If you have received this communication in error, please immediately notify the sender by return email and delete this email from your system