There are usually property damage limits on the policy, so you should check those. But generally, yes, they will pay the expenses directly related to the property damage caused by their insured. I would suggest making a demand in writing and attaching the proposed lease.
The driver will be on the hook for all damages caused by their negligence. Their insurance company is only on the hook for the limits of coverage they provided to protect their insured from his/her negligence. Beyond that, you'd have to get the remainder from him personally.
In Tennessee, the law allows you to recover for all harms and losses you suffer as a direct or connected result of the harmful conduct. However, there could be a possible gap in insurance. Many auto policies have limits on what they will cover, both in amount of coverage, and types of harm. For example, most auto policies do not cover work-related injuries. From the situation you present, it certainly sounds like the damage caused is directly related to the crash, but the driver may or may not have coverage to match it. Yes, you can legally get a judgment against someone for the harm they cause you, but if they can't pay for it, the judgment doesn't mean much. You should consider meeting with a reputable attorney in your area. If the insurance involved is your own, you should consider reviewing your coverage to confirm whether you have coverage for the situation. It may or may not apply, depending on whether the driver has insurance to cover the loss.
The driver's insurance company should be responisble for all your damages, up and to the limit of his or her policy. Have you been in touch with the insurance company?
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