In 1991 the Civic could have had Throttle Body Injection or multi port fuel injection. In either case its not like older carburetor cars where the carburetor float would sink or fail resulting in the car flooding out and stalling.
Does you car run rough before it cuts out. I wonder if your car is actually loading up because it is rich or is it the opposite has your car a vacuum leak and just runs rough causing stalling. If indeed it is stalling because it is rich the probable cause is a leaking injector. It is best to start with the basics. check spark plugs ignition system, adjust valves ensure there are no vacuum leaks ect...