Rear Fuel Trim

The rear oxygen sensor, located after the catalyst, is used for fuel trim corrections on OBD-II vehicles. By virtue of its location, the rear sensor is generally protected from high temperatures and much of the contamination that affects the front oxygen sensors.
In addition, the rear sensor sees exhaust gases that are equilibrated – they have already been converted by the catalyst so that there is very little residual oxygen.
This allows the rear sensor to respond to much smaller changes in exhaust gas oxygen content. In turn, it then possible for the rear sensor voltage to remain near the 0.45 volt switchpoint.

This characteristic allows the rear sensor to be used for fuel control. Under steady rpm and load conditions, the short term fuel trim bias can be adjusted so that the rear sensor voltage is maintained near the 0.45 volt switchpoint.
This ensures that the catalyst is getting a stoichiometric exhaust gas mixture, despite any shift in the front sensor switchpoint.
The rear fuel trim corrections are learned in KAM (Keep Alive Memory).
Internally, this system is known as Fore Aft Oxygen Sensor Control (FAOSC). Note that FAOSC learns and reacts very slowly because the catalyst, with its large/slow oxygen storage and release characteristic, is part of the control loop. Also, this system cannot be used with a "y-pipe" exhaust where a single rear sensor would try to adjust dual front sensors.

Rear O2s if you will are a fine tune of the commanded fuel flow but are very much part of the model used in the PCM's math to correct AFR for closed loop

This means running no rear O2s or Simms will effect how the PCM computes what the fuel trims are.