The short story — and the good news — is that no one will get sick from this batch because no human pathogen can survive in wine. Alcohol and acidity will kill off any bacteria or yeast that could survive in the human ecosystem and make you or your friends and family sick. For example, bacteria like E. coli, one of the most common bacteria implicated in food poisoning, need an environment where the pH is closer to that of the human body, around 7.0. Wine, with much lower pH (higher acid) of around 3.5 and with an alcohol content of 10% or more to boot, is a very hostile environment for the kinds of bacteria and viruses that can make people sick. This is why folks who drank more wine and less water (pH of 7.0) during the Middle Ages were not only doing something enjoyable, they were doing something smart for their health.
“Rings around the carboy” happen frequently in winemaking, especially in fruit wines. I’ve had it happen to me at Bonny Doon Vineyard while making a peach base wine for a distillation experiment, as well as during a plum wine fermentation like yours. I found that as the fermentation level of the “must” changed during the course of two weeks, a deposit of pigment formed on the side of our fermentation buckets as the gasses escaped and the fermentation warmed up then cooled down. It looked pretty gross but the wine turned out fine — we moved the fermented fruit wines out of the primary fermentation containers before any bad bacteria or spoilage yeast had a chance to gain a foothold. This is why it’s so important to immediately rack our brand new wines to containers that are more closed and airtight once the fermentation is over. Without the protective blanket of carbon dioxide
gas produced during fermentation, new wines are vulnerable to oxidative damage, as well as to invasion by microorganisms that thrive in a higher oxygen environment.
If what you’re experiencing isn’t just a ring but is a full-blown film you may have a mold or spoilage “film yeast” issue and the wine may not age very well when bottled, or may even smell/taste funny right now. If that’s the case, you can decide if you like the wine enough to keep it.
“Ring around the carboy” is a common home winemaking phenomenon. Your wine should be totally safe to drink, though if it tastes good enough to make you want to may be another question.