As pointed out in "Another Way to Prove Your Negligence Case Under NY Law," the answer is this: if the accident cannot, as a general rule, occur absent negligence, the mechanism causing the plaintiff's injury remained under the defendant's exclusive control, and the plaintiff was not actively negligent, then the plaintiff can recover under the doctrine of res ipsa loquitur.
In Keyser v. KB Toys, Inc., the plaintiff was injured when several boxes that had been loaded (presumably by defendant's employees) onto 7-foot shelves nearby, fell onto her back and neck. Although the defendant did not call any witnesses at trial that were actually present at the time of occurrence, the jury nevertheless believed the defendant's contention that some other store patrons may have pushed the boxes.
The trial judge didn't buy it, however. In granting a re-trial, the Court held that "[W]ithout such speculative evidence, nothing in the trial record supports anyone other than the defendant being responsible for the happening of the accident."
This is indeed a courageous decision. You can bet that the defendant is going to appeal it.