What happens if someone backs into you in a parking lot?

It depends - was it hit and run ? Were both cars backing or one parked and one backed into it? If the other party is no where to be found, typically your Collision coverage ( if you have this coverage) will pay after you pay the deductible. It may also increase your future rates (and /or loss of discounts for being accident free) - so use some logic if it over $1,000 to repair.