the post cat o2 sensor always looks for a 0.1V swing ranging at about 0.6 or 0.7V - as I showed you a screen grab from my mercedes. The ECU will not adjust anything if this sensor reports a full 0.9V swing at regular ignition cycle. It will illuminate the CEL and throw a 0420 code for 1 bank or if two banks both cats are bad then you also get 0430 code.
The ECU will only slice out about 1% trim at best (in 8 or 12 cyl engines usually of VW) as their exhausts are a complex network of pipes if the rear o2 sensor reports an inefficiency code. In modern units like the newer LE nissans the cat going low slightly (cooling down) can cause the trim to spike a little to reignite the cat. It does not actively go into closed loop again.
The front sensor either o2 or AFR in conjunction with the MAP and MAF is the front line information source to the ECU to adjust fuel trim, The ECU always has its priorities straight - that is to keep the cat happy. Your feel, performance, racing mood is secondary.
You are a bit confused in open and closed loop settings, in a cat converter equipped engine the open loop (warm up) phase is incredibly rich - this is to aid in igniting the cat to working temperature. You will also be shocked to know that the mazda RX8 (a fuel guzzler) has stupidly rich settings in open loop and to get it certified in cali - mazda redid the ECU to add even more fuel in the open loop to get the cat working. The open loop setting if used all the time will seriously shorten engine life as its so much that it can wash the cylinders, rings and pistons clean of oil (actively seen in GDI engines - they even raise oil level)
You say you read that if the downstream o2 sensors set the goal for the front, you are very mistaken, the front sensor reports activity to the ECU as "Im seeing this much of fuel per pulse" its goal is a regular switch between 0.1 and 0.9V. What goal can the rear sensor report? It only sees the exhaust after the cat - if you plot this graph you get very very narrow range of 0.1V switch - indicating the cat is working. If it starts to follow the front switch pattern - it flags the cat is bad. Hence the codes 420, 430 exist. The system remains in closed loop - I can prove it to you too. I have seen, plotted, and repaired a lot of cars with this issue. If you connect any respectable scan tool you will see the air fuel status as closed but the emmissions test as incomplete or failure due to the code.
The crank sensor positioning was very amusing to be honest. please shed some light on it.
