In Chrysler's OBDII implementation, the upstream O2 sensor (the one before the Catalytic Converter) is used to measure the air-fuel ratio. The downstream O2 sensor (the one after the Catalytic Converter) is used to measure the efficiency of the Catalytic Converter.
If your going to replace your Catalytic Converter with a Straight Pipe, you might as well throw away that downstream O2 sensor, BUT you'll have a constant Check Engine Light if you do either or both.
The O2 sensor behind the CAT is there to check the function of the CAT, part of the OBDII mandatory emissions self tests. It compares the O2 sensor response with the response of the O2 sensor upstream at the exhaust. If the CAT is working right, it will change the O2 content as it changes the chemical composition of the exhaust. Thus the OBDII computer can tell if the CAT is working by there being a difference between the O2 sensors.
Remove the CAT, the O2 sensor response will be the same, because the exhuast won't change between the sensors and the PCM will constantly light the CEL to tell you to replace your CAT. Remove the Sensor and the PCM will constantly light the CEL to tell you to replace your missing O2 sensor.
Some people have tricked the system with resister wired into the downstream O2 sensor circuit, but that doesn't always works, because the PCM is smart enough to look for a specific difference between sensors, not just any difference.
Some people say the O2 sensor does have some feedback on the engine performance and is neccessary to self tune the engine well, BUT I've never been able to confirm that, there is no literature describing that, AFAIK the O2 sensor is to check the proper function of the CAT and thats it. I don't know for sure, so its possible your engine won't perform as well without it.
Are you asking because your Removing Your Catalytic Converter? If so, WHY?
I'm a newbie to XJ's, but just about every modern car and CAT is free flowing and work fine with it there. Removing the CAT usually gets you nothing but aggrevation and extra noise, nothing in performance. In fact some cars have dynoed the motor before and after a CAT removal and they lost power after removing the CAT. I don't know if this is true for an XJ, someone correct me if I'm wrong.
If you think your CAT is bad or clogged, do the proper troubleshooting, Clogged CAT's is one of those "Jump to Conclusion" Diagnosis, like a bad PCM that a lot of people make, it very often turns out to be NOT THE CASE.