The short answer is yes, olives do go bad. That said, it usually takes a pretty long time for that to happen if they were in good condition when you bought 'em and they've been properly stored since.
How can you tell if olives have gone bad?
How can you tell if opened olives are bad or spoiled? The best way is to smell and look at the olives: if the olives develop an off odor, flavor or appearance, or if mold appears, they should be discarded. Discard all olives from cans or bottles that are leaking, rusting, bulging or severely dented.
What happens if you eat bad olives?
Eating bad olives can also lead to diarrhea and/or vomiting – typical symptoms of food poisoning. By emptying your stomach, taking activated charcoal, and drinking enough water you can cope with that problem pretty fast. But if the symptoms are really nasty, don't hesitate and go to the hospital!