The figure you offered is insufficient in light of the facts of the case. A demand letter often is the first step in the negotiation process for a personal injury claim.The issue arises in personal injury cases where the plaintiff has incurred damages that exceed the available policy limits of the defendant. In this post, our experienced medical malpractice and personal injury lawyers at TLF cover what happens when you reject a settlement offer. Many personal injury claims resolve through private settlement, with no lawsuit necessary. When you decline an offer from an insurance company, it is an opportunity to commence settlement negotiations. It is also important to consult with a personal injury lawyer if you believe that your settlement offer is unreasonably low. Being involved in a car accident is a serious matter. Open a Personal Injury Claim As Soon As Possible. Hiring a Personal Injury Attorney in San Bernardino.