Critical sensors for fuel trim (before it gets burned):
MAP - Manifold Absolute Pressure sensor.
IAT - Intake Air Temperature sensor. (These two are used to calculate the amount of air going into the engine, and adjusts fuel input accordingly.)
TPS - Throttle Position Sensor. Used to give expected engine loading information. Combined with the temperature/pressure readings to determine expected fuel requirements.
The HEGO (Heated Exhaust Gas Oxygen sensor) is used to form a "feedback loop" by taking an oxygen content signal from the exhaust gas. For 1991-up XJ, it's essentially a special ceramic "air battery" that generates a voltage based upon the difference in oxygen content between a sampled gas (your exhaust stream) and a standard gas (a sample of outside air.) If the fuel is trimmed properly, there should (theoretically) be no oxygen left in the exhaust - I believe the typical trim is to allow a very slight amount of oxygen (slightly lean fuel delivery) - principally since the HEGO measures oxygen content, and doesn't monitor HC or CO (unburned fuel or partially-burned fuel, respectively.)
A failed/failing HEGO sensor can cause poor fuel economy, but the engine controls will usually fail into "open loop" mode, which would be rich fuel trim. This means decreased fuel economy, elevated HC and CO, depressed NOx (in most cases. Not so much for us, we've low-compression engines,) and slightly depressed operating temperatures. If you run rich enough long enough, you'll also get a strong smell of gasoline from the engine oil - pulling the dipstick is enough to tell this. (Extended rich running also results in accelerated cylinder/ring wear, due to oil washdown. More on that if you like.)
Lean fuel trim usually results in a slight increase in fuel economy, depression of HC and CO, increase in NOx (due to elevated combustion temperatures,) increase in operating temperatures, and possible damage to metal engine components (melted/cracked/warped valve heads, melted/pitted piston decks, &c.)
To recap: A "rich" fuel trim condition is usually a result of a failed/failing HEGO sensor (in most cases,) while a "lean" fuel condition would be a combination of a faulty HEGO sensor signal and failed/failing fuel trim sensors (check MAP/IAT/TPS first. CTS after those three check out. Typical culprits on non-EGR engines would be MAP/TPS - for RENIX, you would check IAT first, since it gets crapped up with carbon from the EGR.)
