What happens when a oxygen sensor goes out on a 2001 plymouth neon?

The biggest indicator of a faulty oxygen sensor is a noticeable decrease in fuel economy, along with a rich mixture. Now, this does not automatically indicate that the sensor has failed. Be sure to check all vacuum hoses for leaks as well as the ignition system, check the plugs, (are they fouled?) check the rotor, distributor cap, points, spark plug leads, and condenser (check all of these where applicable) Vacuum leaks and ignition problems are notorious for causing fuel economy problems. It's a good idea to inspect and re-new the vacuum hoses every couple of years anyway. Other symptoms of a faulty sensor are a loss of power, (particularly when accelerating from a stand-still), overheating, and spark plug fouling, both of these are due to an increased rich or lean running condition.