Exhaust Fan Runs With No Power at All!
Some furnaces have more than one breaker

Well, most honestly.  


The Air Conditioning unit has a breaker
If present, electric heating elements (e.g. emergency heat) have one or more breakers
The blower will have its own breaker, typically shared with the electronics on a gas furnace
A built-in humidifier or dehumidifer may have its own breaker
Depending on location, the 24V thermostat transformer may be on yet another breaker


Unrelated, the radon venting system has its own breaker.