Here's what the O2 sensors do.
The first one checks the exhaust for oxigen. If there is too much oxygen the motor is running lean if there is not enof the motor is running rich. So this one effects the motor directly.
The second is after the cat. It tells the computer if the cat is working or not. The second one wants to see a lot of oxygen.
There are plug in chips that will allow you to remove the second O2 because the chip tells the computer that the cat is working great.
I have a friend that was telling me that early chevy trucks have a real problem with the second O2 sencers. So he put the 2nd O2 in a can/box and mounted it under the vehicle. The can/box keeps the O2 clean and the O2 sees all the oxygen it needs. I have never tried this though, he claim it works great!