The person driving through. If you're backing out then you do not have the right of way.
backing out- you have considerably less vision
If you strike him - you are at fault. He can be charged with the No Parking violation but YOU are charged with the collision.
Whoever the police report charges with the accident.
It will probably depend on who was backing out first. The first one backing should have the right of way. Also the driving laws don't officially apply in private parking lots. The insurance companies will look at the collision based on driving laws though.
The car going backwards.
If he was driving forward past his intended parking space to take yours, then he is at fault. Cutting across is not permitted in parking lots although many people do it anyway.
Answer Yes, This is a very common type of automotive accident.
The driver backing up. Unless you can prove the other car was driving unsafly.
The greater fault lies with the person backing out of the parking space. You may still be partially at fault for not driving with due care.
The person who is backing out of the parking space
The person backing out of the lot. Cars in the travel lane have right of way.