Ideally the customer will have insurance to cover the loss.

The storage facility would only be liable if it were negligent -- that is, if it knew or should have known that the other customer was a thief, and continued to allow the person to use the storage facility anyway. The mere fact that they offer this particular form of secure storage does not guarantee that theft or property damage cannot occur.

Most likely, the only person who will be liable for the trailer (if it was not recovered and returned) is the thief. It is reasonable to infer that the thief was caught, so the trailer owner can consider suing the thief or making a claim for restitution as part of the criminal prosecution.