What happens if a cop doesn't issue a ticket for an accident?

My husband was involved in a car accident yesterday. He’s okay. A girl was stopped in the left lane of the road (no turn signals or apparent reason to be stopped). He kept driving on the right side of her in the right lane of the road. After he was ¾ of the way past her car she turned right into his back side, hitting the back driver side door panel area. The cop didn’t issue a ticket though and said the insurance can deal with it. Now what? I’m assuming we will be stuck paying the deductible to have the damage fixed at the very least. Possibly our insurance will go up and get dinged for the accident? Do these things ever actually get investigated where they find the other party at fault?