Strays don’t drop any given loot, only the default bones+arrows+slowness arrows.

When a stray is given items via command blocks, they do not drop them

This goes for at least emeralds and iron chestplates, the two items I tried

Now, very strangely, if you use the /replaceitem command to give the strays the items and you specifically target strays that are not using a certain tag, then strays with that certain tag will drop the items. This makes no sense.

If you target strays with a certain tag, they just drop nothing.