In new game +, bosses like Ghorn (Cauldron instance) no longer drop their legendary weapon loot...

I remember getting it during 1st game, then vendoring it just before starting + ! Now it didn't drop... Not that i really need it, besides it had been a crappy level 5 item and i have more interesting loot to stash (like the DLC and/or all other weapons that now scale with your level), but still...

Also, since in Deathinitive edition, items that exceed your inventory capacity are being stored in tome in letters bearing them inside, could you use the tome for stash to put things in?

The legendary loot only drops for the first playthrough, it was that way in the original version of the game as well.