The rear 02 just tells the computer if the cat is working. So it kinda does control emissions. It will set the ses light and the driver will normally take it to a shop and have the cat fixed. The rear 02 does not control fuel trims directly. The only way it will change the trims is on 01+ cars when the rear 02 is removed they can get stuck in the cat diagnostic mode flooding the car with fuel to see if the cat reacts to this. Since there is no cat or 02 it will not change the reading so it will stay in that mode. I put an 02 sim in mine and no longer have that problem. That method works for some and not for others I do not know why.
