The after cat O2 sensor has nothing to do with fuel trim, or how the ECM controls how the engine runs. Its one and only purpose in life is to monitor the difference between the pre-cat sensor, and itself. Once it detects a diiference above its threshold it trips the old P0420 code, and turns on the check engine light. 99.95 of the time, a P420 code without another accompanying O2 sensor code, like a loss of heater circuit, or some kind of circuitry problem code, the problem is the cat. The O2 sensors in the exhaust manifold(s) are the only ones that affect fuel trim. A spark plug anti fouler will cure the code, heck you can even put one in a straight peice of pipe where the cat used to be, and not get a P0420 code most of the time.