Zero possibility.
The organisms that cause food poisoning can survive in wort, but they cannot survive in beer. The combination of boiling killing almost all microorganisms (it doesn't sterilize but it comes close), low pH, and after yeast has been pitched the presence of alcohol, creates an environment where no pathogenic organisms can survive. The only microorganisms that can have an impact on your beer are beer spoilage organisms, which can make your beer tasty funky and sour (that can be good or bad depending on a bunch of circumstances and your own preferences), but no matter what they cannot hurt you.
Now, it is possible for toxic substances to make it into beer, but not food poisoning from bacteria. Contamination from chemicals, bad water (say, lead or something like that), contamination from equipment, or wort that doesn't get fermented under normal means (spontaneous fermentation can sometimes pick up some enteric bacteria, although even that will typically correct itself with time as lactic bacteria reduce the pH, as seen in Lambics).
The reason why food poisoning is an issue with canning is that many canned foods (when improperly canned) don't have the benefits of low enough pH, and alcohol in particular. Lower pH foodstuffs are a little less dodgy. But like I said above, the boil only sanitizes, not sterilizes, and if you only boil when you can something, things like botulism spores can survive the boil. Hence why you're supposed to can foods in a pressure cooker, which can reach the heat necessary to fully sterilize.
So, the thing to take away is that if you follow proper procedure, no problem. If you're leaving wort unfermented for a period of time, then there's a potential issue. The biggest risk is when you do something like canning real wort, where the conditions are possible for botulism just like canned food. If you're canning wort, use a pressure cooker.
End point is, unless you're doing something really unusual, even if you screw things up you have nothing to worry about.