If your vehicle is showing engine stalls when coming to a stop or letting off the gas, here are the most likely causes and the parts you'll need to fix each one.
When you let off the gas, the throttle plate closes and a bypass valve (IAC) or electronic throttle body must quickly adjust to keep the engine idling. Carbon buildup prevents this from happening fast enough. This also frequently happens as an installation error if an 'idle relearn' procedure is skipped after replacing a dead battery.
Cracked hoses or failing gaskets allow unmetered air into the engine, leaning out the air-fuel mixture. When returning to idle, this lean condition causes the engine RPMs to dip too low and stall. Hoses are also frequently left disconnected after recent engine work.
The MAF sensor measures air entering the engine. If it is dirty (often from over-oiled aftermarket air filters) or failing, it miscalculates the air volume during sudden throttle changes, leading to improper fueling and a stall.
The Exhaust Gas Recirculation (EGR) valve is supposed to close at idle. If carbon buildup causes it to stick open, exhaust gases flood the intake manifold and choke the engine of oxygen when coming to a stop.
In automatic transmissions, the torque converter locks up for highway cruising. If the solenoid fails to unlock it when you slow down, it acts exactly like forgetting to press the clutch pedal in a manual car, violently stalling the engine as you stop.
A weak fuel pump or clogged fuel filter may struggle to maintain the correct fuel pressure during the rapid engine vacuum changes that occur when decelerating, starving the engine of fuel.