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When overcurrent occurs and does not trigger a breaker, it can create a significant fire hazard. Circuit breakers are designed to protect electrical systems by interrupting current flow under fault conditions, such as overloads or short circuits. If an overcurrent condition persists without tripping the breaker, the wiring and connected devices may overheat. This overheating can ultimately lead to insulation failure, molten wires, or even ignition of nearby combustible materials, thus posing a severe risk of fire.

The other options do not accurately describe the concerns associated with an untripped breaker during an overcurrent event. Failure to trip would certainly affect the circuit negatively, and while a breaker may experience wear and tear over time, not tripping under overcurrent cannot be viewed as a means to prolong its life. Moreover, the situation is far from being safe or normal; it indicates a malfunction or an alarming condition within the system that requires immediate attention to prevent potential hazards.