Loud rattle coming from the bottom of engine. mostly heard after letting off the gas, starting and shutting off the vehicle.

Very hard to know without actually hearing the vehicle but,,,With what you describe,the cat/converter 'may' be making the sound.With the car off and engine cool,get under and give the cat/con a really give shove or hit.The insides of them do corrode and the internals make a very loud rattle.If this isn't the problem it will let you see if there is a loose exhaust mount that may also make a rattle.(The cat/con sound is like there is a very loose metal plate hitting something)Its actually the internals of the cat. that have broken loose and rattling inside it.Hope this helps