It may be possible, depending on your circumstances, to re-register a written-off car. The option to re-register a vehicle is available in most states and territories. So, you'd need to check with the roads and transport authority in your area to find out what you have to do. For example, written-off vehicles in Queensland can only be re-registered if they've been fully repaired, and have passed a Queensland safety inspection and a written-off vehicle inspection.
However, in New South Wales, written-off vehicles cannot be re-registered except in very limited circumstances. To be re-registered in NSW, your car must not have any non-repairable damage, and must also fit into one of the following categories:
The car was hail damaged, and you were the registered operator for more than 28 days before the damage occurred.
The vehicle was inherited from a will or letters of administration.
It was registered in your name for more than 28 days before the damage occurred.