Naaaa, it will bring way more than $50 at an insurance company auction. Look at www.iaai.com or www.sapulpapool.com to see what I mean. Unless it’s really hurt bad, it should easily bring more than the $1635 difference between the $8000 damage and cash value of the vehicle. I think they should probably total it at your request.
On another note, since you were rear-ended into another vehicle, the accident is not your fault. The OTHER GUY’S insurance should be paying for your vehicle, and they should want to make you as happy as possible as your neck and back still hurt a week after the wreck.