Can a breaker be bad but not tripped?

Yes, an individual circuit breaker can go bad or suffer internal mechanical failure while remaining firmly in the "On" position without tripping. This dangerous failure mode typically occurs when the internal spring-loaded contact points become pitted, oxidized, or welded together due to age, power surges, or heavy electrical arcing. When this happens, the breaker may fail to automatically trip and interrupt the flow of electricity during a severe overload or dangerous short circuit, which removes the vital protective barrier designed to prevent electrical fires. Alternatively, a broken internal mechanism can cause the breaker to remain switched to "On" outwardly while internally failing to conduct electricity, leaving downstream outlets completely dead despite the toggle position. You can troubleshoot electrical safety safely by testing terminal output with a multimeter. You can verify that your corrective action is successful when having a licensed electrician inspect the panel and replace a compromised breaker restores proper protective function.