Is a property manager liable for damages done to a vacation rental property?

You could sue the property manager for negligence.  Negligence is the failure to exercise due care to prevent foreseeable harm.  Due care in this case would be that degree of care that a reasonable property manager would have exercised under the same or similar circumstances.  You would have to prove that a reasonable property manager would have checked the premises to see that the refrigerator/freezer door was closed.  After establishing a duty of due care, you would have to prove that the property manager breached the duty of due care by failing to close the refrigerator/freezer door.  You would then have to prove causation; that the failure to close the door was the actual and proximate cause of the damage.  Actual cause means but for the failure to close the door would the damage to the floor have occurred?  If the answer is no, you have established actual cause.  Proximate cause means are there any unforeseeable intervening events which contributed to the damage to the floor?  If the answer is no, you have established that the property manager's failure to close the refrigerator/freezer door was the actual and proximate cause of the damage to the floor.

You have now established the property manager's liability for negligence.  Your damages (the amount you are seeking to recover in your lawsuit) would be the cost of repairs to the floor.  You will need to mitigate (minimize) damages by not selecting the most expensive repair service.  In order to mitigate damages, you should select a floor repair service whose rates are comparable to other floor repair services in the community where your vacation/rental home is located.  If you do not mitigate damages, your damages will be reduced accordingly.