If your vehicle is showing metallic rattling noise from the engine bay when decelerating, here are the most likely causes and the parts you'll need to fix each one.
Thin metal heat shields around the exhaust manifold or downpipe frequently rust at their mounting points. During deceleration, the engine hits a resonant frequency that causes the loose shield to vibrate loudly against the exhaust pipe.
On turbocharged vehicles, the internal wastegate linkage wears out over time. When you lift off the throttle, the lack of exhaust pressure causes the loose wastegate flap to flutter and rattle against the turbine housing.
If the exhaust was recently removed for service, the bolts or tension springs connecting the exhaust flanges can back out. Engine braking shifts the exhaust, causing the loose flanges to rattle against each other.
Worn mounts allow the engine to tilt excessively forward or backward during engine braking. This shifting can cause metal engine components or the exhaust to make contact with the chassis or subframe.
The timing chain tensioner keeps the internal engine chain tight. When decelerating, the load on the chain shifts, and a weak tensioner allows the slack chain to slap violently against the metal guides or timing cover.