Typically exhaust fans do not need to be shut down. Over 2k cfm supply fans do need detection and automatic shut down. Engineered smoke control systems require a Rational Analysis Report which will dictate if exhaust fans need to shut down, but usually no-one cares if it does not affect pressure differentials required for smoke-control.
During a fire event if hot smoke and gasses are exhausted that is a good thing, but if the fan is not rated for high temp, served with e-power and in accordance with CBC smoke-control requirements, it is acceptable to let the fan die on its own.