Insurance companies class vehicles that have been damaged completely beyond repair in accidents as total write-offs. They should not be returned to the road for safety reasons.
The main reason for not putting the vehicle back on the road is that no one can predict how it will react in another accident.
A car that is classed as a write-off because it is "beyond economic repair" is different. These vehicles are written-off because the cost of fixing the vehicle is higher than the value of the car, or not economically viable for the owner or insurer. However, the vehicles can still be repaired.
So, for example, your car might be worth €10,000, and if you crash it and it costs €14,000 to repair, an insurer will classify it as a write-off "beyond economic repair".