What does bank 2 sensor 2 o2 sensor do?

Usually each side or bank has a sensor that monitors o2 in exhaust and adjusts run time on injectors, sensor 2 is usually behind convertor and may be shared by both sides, it monitors efficiency of catalytic convertor. I would replace sensor first since they are cheap and appears you have no problem with the ones controlling mixture. Only running excessively rich (raw fuel) will prematurely kill a convertor and under normal conditions they never wear out. Look more closely at that after you have ruled out sensor.