When I first got my truck I had a rattling cat at idle and no matter how much I tinkered with the heat shields it wouldn't go away and I was afraid the honeycomb started to shatter. Turns out it was a small, notecard sized plate that was tack welded right behind the cat, on top of the exhaust (I assume it was an ID plate of sorts) and one of the welds broke off. Ripped it off and never heard it again
A near dead cat will rattle almost constantly (especially on revs, as opposed to idle) and very obviously sounds like something getting blown and thrown around inside the exhaust - not a very consistent noise, in terms of how/when it starts to rattle. You would more than likely have a code thrown for the cat or O2 sensors, too