The rear O2 thing got my curiosity so I cut an pasted a few things below. After some searching I found that the major function is a cat check, but it can figure into the fuel trim calculation.
Fuel trim refers to adjustments being made dynamically to the base fuel table to get the proper ratio of fuel to air. Short term fuel trim refers to adjustments being made in response to temporary conditions. Long term fuel trim is used to compensate for issues that seem to be present over a much longer period. Fuel trims are expressed in percentages; positive values indicate lean (add fuel) and negative values indicate rich (subtract fuel). Fuel trim banks refer to the cylinder banks in a V style engine. Cylinder #1 is always in bank 1. Fuel trim is generally calculated by using a wide set of data values, including front O2 sensors, intake air temperature/pressure (or the more elegent air mass sensor), engine (coolant) temp, anti-knock sensors, engine load, throttle position (and change in throttle position), and even battery voltage can effect fuel trim. Long term fuel trim generally should not exceed +- 10
The rear O2 has a mininumal part in the calculation in OBD-II, maybe none depending on the software. Jerry updated the software in my EEC to a later version when he reflashed it back in early 2002.
Rear Fuel Trim
The rear oxygen sensor, located after the catalyst, is used for fuel trim corrections on some 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. 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.
There is a TSB also on O2 sensors: http://v8sho.com/SHO/TSB0197HO2SServiceTips.htm