The answer is "yes." If you suffer an injury while shopping or receiving retail services, you are protected by laws requiring retailers to ensure anyone in, or on, their premises is safe from harm. If you are injured in a retail establishment, the property owner and/or manager may be liable.
In most personal injury cases, the question is on who was negligent. For example, in a car accident, it is the driver who was speeding, texting, driving drunk or otherwise not paying attention to the road who is responsible for covering the costs if anyone is injured.