Heres what I'm aware of. I played Farin all the way through the end without switching.
The next playthrough from the start of the game, I played the Elf Loremaster.
What I found in her inventory was all items "found" but "not equipped" by Farin. But, if I go back to Farin during this new game, I also found he still has his best equipment on from the end of the last game. "If I switch to him"
That said, items that arent equipped "should" show up at least when you start a new game. I can't say otherwise because at first I only played Farin. As far as given items, everything that I gave to the other characters didnt show up in there inventory the next playthrough. So, my best guess is the AI characters will only still have it if they choose to equip it. Otherwise it will be lost. I also found if you don't give the AI players anything they will upgrade with the best that they can find, at certain times during the game. I did fine all the way through the game, barely giving anything to the AI characters.
Here is something cool I found out though. One of my Gold epic weapons from Farin that he didn't have equipped I was able to give to the AI version. Since it is a much better weapon, it was an instant equip, the AI Farin still wields. For now, if I "play" Farin he also shows all the weapons I used from the last game. That said I could uniquip armour and weapons switch to another character, and then give them back to the AI version of Farin. It's still possible I think though, that I could loose items, if I give the AI Farin items lower than what he has/has equiped. It could just be that my playable version of Farin still has the sword I gave the AI, because he chose to wield it right away, and then I switched back to him right away afterwards, while he still had it equipped.
Did I confuse you yet?.... I hope not Give it a try. Any questions and Ill try to explain myself better.
Alltogether, I think what it is is that the AI and playable version of characters equip differently, but this is sort of a loop hole for getting favorite items equiped onto your AI, while not taking them from your playable character. Just make sure to switch back as soon as they equip, and the game might even have to SAVE first. So dont quit until you see that rotating loading ring at the bottom. Still not 100% sure on how all this worked out. But, it seems to have worked so far.
So, just be careful what and how you sell/give, if its something you prefer to use on another character.
*My only wonder is that I couldn't give 2 of 4 shields to Farin that he previous found, and equipped at times (and they were the cheaper ones. It seemed odd, but I think something may have happened to his stats at the start of the new game to cause this.Or it could just be that the AI turns down lower items if they have something better.