This is a big problem in Texas and Oklahoma. If the other driver has no insurance, your attorney can seek a judgment against him or her and go after any money or nonexempt property they have. However, most of the time if the other driver does not have insurance, he does not have any assets.
Hopefully, you will have insurance that will cover some of your medical bills. Hopefully, you will have uninsured motorist coverage on your liability insurance policy that will cover some of your losses.
If you do not have any insurance coverage or money, you may end up on medicaid. This is not a good solution. Sometimes it is the only one.