Is it permissible, in Islamic law, to file a compensation claim against the governmental fund for the death of a mother in a car accident where the driver was unknown?

If an accident results from the driver's negligence, then he and his 'Aqilah (male relatives on the paternal side) bear the compensation. The injured party may take his right from an insurance company, or a governmental or private fund. If what the lawyers present to you is truly your right, then there is no objection to applying to the governmental fund according to legal procedures, without deception or fraud.