First of all, as is talked a lot about on this site, solely because you fall does not mean the business establishment owes you anything, unless you can show they were negligent and that negligence was the legal cause of your injury. You would have to show damages as well. Here, it is stated that the person who fell broke their arm, and that generally is an injury that would result in medical bills as well as pain and suffering. Thus, the answer here is that if the supermarket was negligent and that negligence is the cause of the broken arm, then generally this would be a case.
Every case must be decided on the specific facts and the advice in this blog is of a general nature. The advice in this blog is intended to be general in nature and should not to be construed as specific advice for a case, as the most slight difference in the facts could ultimately change the result. Also, this blog is based on Florida law and the laws of any other states or country could vary significantly from Florida.