If your boyfriend rear-ended a vehicle then it would appear that the accident and resulting damages were his fault. Since he was driving without insurance at the time of the accident he is being held personally liable and responsible for the damages he caused to the other party.

The other party appears to have made a claim with their insurance company and was paid out for their damages in the amount your boyfriend is being billed for, the $11,000. The insurance company is now charging your boyfriend for the monies they paid out, this is called subrogation. They are allowed to due so since your boyfriend was at fault for the accident and thus can be held accountable for the cost of the damages he caused.

The insurance company can request that your boyfriend pay since he was at fault and was uninsured and thus does not have an insurance company to reimburse the other party's insurer for the monies they paid out. If he does not pay or negotiate a payment plan then the insurance company can then take him to court to seek a judgment against him, however they do not need to get a judgment to request it to be paid since as an uninsured motorist he is being held personally responsible for the accident. If he chooses to ignore the payment request then the insurer will likely proceed with filing a lawsuit against him.

Uninsured motorist normally covers bodily injuries though some states do have uninsured motorist property damage policies that drivers can buy. So if the other party had an uninsured motorist property damage policy or collision coverage it should indeed cover the damages your boyfriend caused. In fact if the insurance company is subrogating with your boyfriend then it would appear that they already paid out a claim to their policyholder under one of these coverages, that does not however take away the responsibility of your boyfriend to be held accountable for causing an accident.

State laws vary however most all allow a party hit by an uninsured motorist or their insurance company (if they have paid out a claim) to go after the at-fault driver for the cost of damages. If the uninsured motorist does not come to an agreement with the other party or their insurer to pay for the damages then normally the state will penalize them by suspending their license, registration, etc.

For example in Florida the insurance regulator notes that if you are at fault in an accident while driving without insurance you should negotiate with each person that sustained property damages to obtain releases for their damages. If the person is insured, you should negotiate with the person's insurance company as the company assumes the rights of compensation since they have reimbursed the insured for their loss.

If you are unable to pay the amount of damages in full, you may pursue a monthly payment agreement. In Florida with the insurance coverage and releases or monthly repayment agreements, you will be able to provide them upon notice from the department to avoid unnecessary suspensions of your driver license, tags, and registrations. Your boyfriend can contact your state's DMV to find out what penalties he could be facing for driving without insurance and if he does not come to an agreement with the insurance company for repayment.