What happens depends on a few things. One, what state do you live in? Two, does the lady have collision coverage? Three, does the lady have Uninsured motorist coverage?
If the lady has Uninsured motorist coverage, then HER auto insurance company will cover her for bodily injury and her property damage to her car if a driver hits her without auto insurance. That is the purpose of uninsured motorist. Half the drivers in California drive without auto insurance. That is why people that have auto insurance usually have uninsured motorist coverage on their auto insurance.
Was the lady driving a newer car ? Or an old car? People with newer cars usually have collision coverage and uninsured motorist coverage. People that drive old cars usually don't. So, the kind of car she was driving, new or old, may be an indication of what kind of insurance coverage she has.
And, if her auto insurance company pays for her damages, they will put you in collections to get their money. Or, at least try to get their money back.