This question would require much more information to be answered. Very possibly the owner of each vehicle could be responsible for their own damage. Consider seeking legal advice.
If the car is parked illegally, its driver will be considered at fault. The thinking is that if this person hadn't parked illegally in the first place, the accident probably would have been avoided. Traffic laws vary from state to state, however, so its best to check with the state where the accident occurred traffic laws.
Of course it is your fault. The fact that the car was illegally parked is of no consequence. You didn't look where you were backing or you would not have hit the parked car. Would you have hit this car if you had been looking? Perhaps the illegally parked car is a Mini Cooper, parked illegally 1 foot behind a Hummer and therefore not visable when the driver looks before backing up...
As long as the parked vehicle is parked properly and not illegally parked in any manner, then the vehicle that rear-ended the parked car is at fault. Now if the parked car is sitting illegally (such as double parked or parked in a no parking zone, etc.) then the parked car is at fault or even both the parked car AND the car that hits it are BOTH at fault.
The driver of the moving vehicle. It's impossible to assess liability to an inanimate object (in this case, a parked car). And, certainly, it's aggravating when an illegally parked car is blocking the way. That's probably why it's illegal to park there, anyway. But... 1. It doesn't give someone the right to hit the parked car and, 2. A person operating a vehicle has a greater duty to make sure the way is clear. Recently, one of the larger insurance companies has been assessing liability to the owners of parked vehicles (for instance, a vehicle that has broken down and is, for all practical purposes, parked illegally on the side of the road or blocking traffic). To date, that company hasn't won a single arbitration to support such a liability decision.
Yes, it is. Liability can't be assessed to an inanimate object. The owner of the illegally parked car isn't inanimate, of course, but it would still not give the driver of the moving vehicle the "right" to hit the parked vehicle. As I noted in a similar question, recently one of the larger insurance carriers has been applying fault to the owners of illegally parked vehicles. To my knowledge, that carrier hasn't won a single arbitration for doing so, and has been forced to pay the claims in full. On the other hand, there could be certain circumstances where negligence -- or, at least, comparative negligence -- could be applied to the owner of an illegally parked vehicle. For instance, the car is parked on a blind curve in a no-parking zone, or of course it's parked illegally and has endangered public safety (in front of a fire hydrant, for instance). If, however, this is just a case of a driver striking an illegally parked car because the car was blocking his way, or the driver was going through a parking lot and didn't expect to see the parked car, the driver would be found at-fault. Look at it this way: Every driver of a moving vehicle has to be cautious and prepared for the unexpected. Suppose it wasn't a parked car, but a kid on a bicycle or a pedestrian. In that sense, "right-of-way" takes on a whole new meaning.
Generally speaking, the driver in motion is considered to be at fault when a parked car is hit, even if the car was parked illegally. The exception to this would be if the car was parked in a dangerous, hard-to-see location and the driver in motion could not have reasonably avoided hitting it. For example, if a car is parked on a sharp curve in the travel lane of a narrow road, and the driver of a car driving around the curve at the speed limit would not be able to see the parked car until too close to it to avoid a collision, then the driver might not be liable for damage to the parked car, and indeed the driver who parked the car might be liable for damage to the car that hit it.
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