1) If a person was involved in an accident and the damages are greater than the amount of insurance available. Is the injured party permitted to sue the mazik in secular courts for amount in excess of the insurance?
2) If the accident resulted in loss of life c"v may the family of the victim sue the estate of the mazik in secular court for amounts in excess of the insurance?
Answer:
It is forbidden to sue another Jew for damages in secular courts, unless one first makes an attempt to claim the damages by means of beis din. If the person in question refuses to come to beis din, beis din will grant permission to sue in court, and only then is it permitted to do so.
In spite of the great tragedy of loss of life, the Torah does not grant monetary compensation to the family of a victim. Therefore, one would not be permitted to sue (a Jew) in court for amounts in excess of the actual monetary damage incurred. It is only permitted to make claims in secular court, with permission from beis din, for money that one is owed according to Torah law.
Sources: See Shulchan Aruch, Choshen Mishpat 26; concerning collecting money in excess of the money owed, see Shach 15, who forbids collecting the extra sum even when the parties agreed voluntarily to go to court; Maharsham (1:89), however, writes that under certain circumstances it would be permitted to collect the extra sum, but even he would concede that one may not lechatchilah make such a claim in court.