It always was that if your own company write it off then they buy the car, if it's the third party insurance company then they remove the value of the scrap from the valuation and pay you that leaving you to dispose of the car. Or that's what it was.
Write off just means that it's cheaper for them to pay you the value minus the scrap than to repair. It has been a few years since I worked in the evil industry
Easiest solution is to call your company and tell them that's what's happened and ask them what it is they will want to happen. Could be as simple as letting them know when it's back on the road.