Many times, victims of auto accidents are approached by the person that hit them who asks that the police not be called. They promise a quick cash payment or to have their insurer fix damage to the vehicle.
Often, however, these perpetrators will change their story after leaving the scene. They may give an untrue version of the facts at a later date. This makes it very hard, if not impossible, to make the negligent party pay.
If you are in an accident, make sure you comply with all state and local laws, including ones that require you to report an accident to the authorities. In my experience, a police investigation is very helpful to injured victims of accidents. Police will determine what, if any, insurance coverage the negligent party has, and provide this information in a report. And if the person who injured you violated any traffic laws, they may issue a citation.
Remember- if you are in an accident and are in a vulnerable position, and someone offers you an on-the-spot deal that sounds too good to be true - it probably is.