I have a digital thermostat and the fan will blow out air whether it is in off position or auto. It will run a long time and shut off occasionally but come back on. I have even turned the main switch off at breaker panel and it still runs?? It blows cool air. I have just changed the filter. The thermostat is turned off for heat and cool both but fan still blows. Help please!

I have a digital thermostat and the fan will blow out air whether it is in off position or auto. It will run a long time and shut off occasionally but come back on. I have even turned the main switch off at breaker panel and it still runs??? It blows cool air. I have just changed the filter. The thermostat is turned off for heat and cool both but fan still blows. Help please!
It's normal for the fan to run and the air to blow until the air flowing is of an average temp, how long does the fan run after you turn the fan off at the thermostat or at the breaker ? If it's more than 5 or 10 minutes, then something's wrong, what, I don't know, sorry but that's all my limited experience will let me advise you.

It is imposible for the fan to run if you turned off the correct breaker, or you have very big electrical problems.

Right. Usually the blower runs off a single pole breaker, not the double pole one for the outside compressor.