Answer:
Jack can sue Client A for negligence and in order to do so, his lawyer would base the claim on vicarious liability. Under vicarious liability, a tort must be committed by an employee of Client A (the employee that negligently placed the boxes in the hallway without telling Jack) and the tort must have occurred during the course of employment (Jack was cleaning Client A's hallway and the employee was working for Client A at that time).
Vicarious liability is a secondary liability because the employer did not cause the tort directly, but his/her breach of the duty of care resulted in the negligent act that injured Jack. E.g. someone working for a utilities company accidentally injures a bystander by dropping an iron tool on his feet and breaking it. The utilities company didn't directly caused the injury, but an employee did while working for them.
Jack will likely recover pecuniary damages that cover the lost wages resulting from him not being able to work and other costs related to the injury. Depending on how serious the injury was, and how painful it might be both right away and in the long run, Jack might also receive compensatory damages for the injury suffered.