Who is responsible dog owner or grooming salon/store when an employee gets bit and comes close to death from dog bite?

Either or both could be liable for some or all of the damages if they are deemed to have been negligent, and that negligence is deemed to be a proximate cause of the damages (although the employee may not be able to sue the store owner under workers' compensation rules; the pet owner may be able to get contribution from the store owner if he/she has to pay the employee any damages.  For example, in the following example, the pet owner, store owner, and employee could each be held to be 1/3 responsible for the damages (but a jury could find them responsible in different proportions).  Pet owner fails to apprise store owner that the pet has a history of sometimes biting.  Store owner fails to take adequate safety precautions, such as shorter leashes, which, if employed, would have prevented the incident.  Employee's actions also contribute to the incident because he was teasing the dog by holding out food and then snatching it away.  In such a case, assuming that the employee suffered $21,000 worth of damages, if he is held comparatively negligent for 1/3 of the damages, he would recover $14,000 from the pet owner (not from the store owner because of workers' compensation rules), out of which would come his attorneys' fee (assuming the attorney was working on contingency) and all expenses (filing fees, court reporter costs, etc.)  In turn, the pet owner would recover $7,000 from the store owner.