What would cause engine to idle rough and die when car slows down or stops?

Answer 1

It depends on what kind of car you have. Three things are needed to "make fire" in the engine: fuel, air, and spark. If any of these is interupted then it can sputter or just not run. How those three gets there depends on the car. Older, carbureted engines mixed fuel and air in the carburetor and then moved them into the piston. Fuel interuptions would happen at the carburetor. Air interuptions rarely happened, but could be because of poor settings inside the carburetor. In newer engines the air and fuel are brought in separately. A sticky fuel injector, low fuel pressure, or a computer problem can cause rough idling. How the "spark" gets into the cylinder, via spark plug, has not changed much. What triggers the spark has. In older cars it could be a mechanical distributor/rotor/points system. If there were debris in there, or even poor spacing then the engine could rough-idle. In the newer systems its all computer controlled or hybrid. It could have a weak or discharged battery. It could have a weak alternator/generator. It could have a clogged air or fuel filter. There are a lot of things it can be. A quick inspection can tell a qualified mechanic what the problem is. How he goes about determining what the problem is and how to fix it really depends on the type of Car.

It could be something as simple as a fuel filter! Try that.
Then spark plugs and wires. Air filter.

If those check out fine or you have replaced them. Check for stored trouble codes or an illuminated CEL.

It could also be a Idle Air Controller problem, if they get dirty they can stick. Also, on computerized cars, crank and cam angle sensors can go bad. Lots of things here.