The problem you are experiencing may be from a wire short or more commonly from cavaliers of that age is a fuel pump failure. The problem the other comment refers to is the TCC solenoid. It is an electronics switch in the torque converter allowing is to lock up at around 55 kilometers and hour depending on how hard your pushing the car. This gives you overdrive allowing for higher speeds and better fuel economy. After many years this switch malfunctions and will not release the torque converter from lock witch it needs to do for the engine to idle at stop. If the cavalier is stalling in a violent manner than it is most likely the TCC solenoid. Yes this problem can be solved by simply disconnecting the switch, but it will be at the cost of fuel economy and highway performance. I hope I have been of some help to anyone with this problem.
I hate to hear this about a Cavalier. I've had three and ran the wheels off them with nothing, but good luck. Mine is over 200,000 now and she needs brakes, rotors, struts, and shocks, but it is from overuse and abuse, not from malfunctions. We have replaced a water pump at 150,000 miles and a couple of belts. We also are having the fuel filter leak that is need of repair. You can't Condemn the car for normal wear and tare and that is all my 1992 has had wrong.
My first Cavalier was a red 93 Convertible. It has an automatic transmission. I don't know if you said yours did. My car started stalling first when backing up from parking spaces first thing in the morning or anytime it sat for a few hours, then it went from that to also stalling at the first few lights or stop signs. It would be fine after a little bit of driving. After it got pretty bad, my granddad came down to rescue me one time with a can of WD-40 and sprayed the coil pack. Never stalled since. I think he said there was water on it or something, but I'm no mechanic. One of these comments aught to help! :)