In the event of a vehicle accident lawsuit, you will be required to pay the costs yourself. Although most attorneys will work on a basis of no money successfully received they won’t charge you. A lot will depend on the individual case, and they will not take on a case they don’t think they will win. When determining what amount to claim for the accident or injury which hasn’t been paid for by your insurance company, you need to address this issue as you can’t raise the stakes later. You can however make a claim that says “with costs”. If your insurance company decides to sue the other party, you will not however have to bare the costs. That will be their liability.
For more info, see How to Write an Auto Insurance Settlement Demand Letter