Sleepy spells it out pretty clear how your insurance company is supposed to work for you; that they cover your loss then it's up to them to try and collect back what they paid out from the other guy's insurance company.
Also, like sleepy pointed out, an insurance company is not going to settle one single dime unless and until you sign off that the debt is paid free and clear, regardless of the max coverage their client paid for. It is their fiduciary responsibility to represent their client for the full loss, not just up to what their client paid for. That's for a civil claim. For a criminal claim a judge can provide a sentence that includes financial restitution for the victims. If a case goes to court and there is a judgement providing this restitution, know that the civil settlement with the insurance company does not forgive that judgement and the convicted still will owe that restitution.
For me, my loss was more than the minimum coverage of the other party's insurance, so my insurance company, which covered my loss, wasn't able to collect the full loss they paid on. The judge however provided me with a financial restitution. If and when I ever collect on that, I'll have to pay back to my insurance company any money they paid on the claim but were unable to collect on. Insurance companies can not be awarded restitution in criminal cases; they are not considered victims. It's part of their doing business to run the risk of the loss. However, I am not allowed to collect twice on a loss; from my insurance and from a court order.