Auto Insurance Claims: Rear ended- old car, chevy cavalier, something in mind

Question
My sister was read ended Friday night by a large SUV with a front grill guard.  The other driver admitted fault and was issued a ticket.  She went to the emergency room to be checked out and is since just sore.  Her car is a 1995 Chevy Cavalier and not worth much money.  Her bumper is badly dented, her trunk is bent, and her frame is buckled.  She is in college and doesn't have the money to buy a new car.  I am afraid they will total her car and she will be left with not much money and no car.  What can we do to ensure that she doesn't end up worse off than before the wreck since it wasn't even her fault.  The father of the other driver offered to just write us a check for the damages, but we have already called their insurance company.  Is there any way to not have the claim filed and just let him write us a check?  Please help.

Answer
This is a duplicate question, but I did want to add something.

If you are considering taking the check from the individual to keep the car from being a total loss, please keep something in mind.
You mentioned that the frame was buckled.  A Cavalier doesn't have a frame.  It is a unibody car.  It does have rails that in the rear that the rear bumper, body panel and floor weld to and all of these parts work together to absorb the energy from an impact.  If these parts are already damaged and she continues to drive the vehicle without repair, then the vehicle will not be able to withstand another rear end collision as well.  This is an important safetly issue as the gas tank will be much more as risk of rupturing in a future collision.