2006 cobalt 2.2 The fan stays on even when car is off, removed fan 2 relay to turn it off

Your car probably has a coolant temp sensor that is probably the cause. Replace it.

The fan relays also could be going out. Mine went out and shorted out the entire wiring from the relay to the fuse box and motor. I just replaced everything. I have a built up engine so it runs hot. I bypassed the temp sensors and have them run all the time. I have it wired to the ignition so when I turn the key on, the fans come on. If you don't want that, have the sensor and relay checked and replaced. There are good one, and not so good ones. I suggest spending more money for the top relays or sensors. Another $15 will same a call to the fire department.

I also had a second set of fuses placed in line with each of the fans, so if one shorts out, I still have the other to work.

Did you get it fixed? Have you had all your recalls taken care of? If not please have recalls done ASAP.