If there is no fault, then by definition there is no negligent party - negligence implies fault.
You need to be more specific about where the loss occurred. If it happened in a no-fault jurisdiction, your right to sue is typically more limited than in a tort jurisdiction.
the driver at fault
You can.
You can sue in most jurisdictions
If the accident was your fault, the other party's insurerhas no duties owed you.
yes you can
If you are involved in an accident that is not your fault you can sue on several grounds. Damages to the vehicle if you owned it. Medical bills if injured, pain and suffering, lost wages, etc.
Because the person who hit them is at fault and with rear end accident there is usually medical bills and pain involved with the people who were hit. They have the right to sue to recover from the accident.
Sue
Well Someone will sue you and the insurance will do something about it!
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