2002 Mercury Cougar car shuts off r

The course of action depends on whether the engine is stalling due to a sensor failure or due to low idle speed. With low idle speed, you can keep the engine running by holding the accelerator pedal down 1/4". If it's a sensor failure, there are some that commonly fail by becoming heat-sensitive, then they work again after they cool down for an hour. They typically will not let the engine be restarted right away. Most of the time a sensor failure will last long enough, as the engine coasts to a stop, to be detected by the Engine Computer. It will set a diagnostic fault code indicating the circuit that needs further diagnosis. The place to start is by having the diagnostic fault codes read and recorded. The people at many auto parts stores will do that for you for free.