More input - is this RENIX (1987-90,) OBD-I (1991-95,) or OBD-II (1996-2001?) If it's OBD-II, which sensor are you talking about pulling - the one in the exhaust manfold, or the one in the pipe after the catalytic converter?
For the "downstream" HEGO (after the cat, 1996 and up,) that sensor is used to provide feedback as to whether the catalytic converter is running - disconnecting this sensor can eventually result in "throwing a code" - the ECU will tell you that either the downstream HEGO or the cat itself is shot. There are simulators that will fool the OBD-II ECU into thinking that everything down there is just ducky - check with Summit or Jeg's.
For the "upstream" HEGO (the ones in the exhaust manifold, regardless of year,) the ECU will not be able to enter "Closed Loop Operation" - where the fuel inejction system control is augmented by the feedback signal after combustion. If the sensor is unplugged, the effects are unpredictable (but I believe it tends to result in "False LEAN" signalling.) If the sensor is removed and allowed to hang free - but remain connected electrically - you will get a false LEAN everytime the system tried to go into Closed Loop - and you will get a code for HEGO failure (most probably) or Closed Loop Failure (second most likely.)
The false LEAN signals will typically result in decreased fuel efficiency, since the ECU will read excess exhaust oxygen and attempt to compensate by enriching the AFR. In extreme cases, this can result in a loss of power - and the reduced mileage will be readily noticed.
Failure to enter Closed Loop operation will also be likely to cause a code, and will result in decreased power and fuel mileage.
Having said that, why is it everyone lately is asking about disconnecting critical sensors? I can see working to modify a few outputs (CTS and IAT come to mind,) but there is no sensible reason for pulling the upstream HEGO, so why do it?
The point of fooling the ECU in certain instances is to increase power, but pulling the HEGO does not accomplish this. It also throws the system into a tizzy - it can't keep track of what it's doing very well.
If you are looking to modify electronic control systems in order to make more power, it would be a good idea to research such systems before throwing out ideas to modify them - especially since these ideas usually sound silly, and you really don't need to make large modifications to get results! Search around, spend some time at the library, and you'll be able to not only answer your own question - but understand just why these things work the way they do! I'm not a huge fan of electronic controls, but I've made an effort to understand the systems on my own before I start playing about with them.
You can find decent books on the subject of electronic controls in general by Haynes and Chilton (I didn't say they were GOOD - just decent,) and a little research into the publishing lines of Mitchell, Motorbooks, HP Press, Bentley Publishing, and other automotive specialty publishers can get you information that would be invaluable.
I'm not trying to sound like I'm coming down on this idea - at least, not on purpose - but it seems like a lot of silly questions have been coming down lately, and I'm just trying to do my bit to slow them down. There's nothing wrong with asking questions - but you really should do a bit of preparatory research into the subject so you will understand the answers. I don't see a point in answering someone with a question about modifying a system when they make it clear they don't understand enough about how it works to understand why the mod will or won't work - and there is a LOT of information out there!
[/RANT]
5-90