At least, a new pitfall for me
What happened.
While going through Dragon Spire, I realized that I forgot the Shroud in the town. "Does not matter", I thought, "Erathsmedor is, in fact, 'outside' the dungeon so that I'll be able to set a portal after 'leaving' the dungeon and go for the Shroud". I continued through the dungeon, entered Erathsmedor's area, created the portal and teleported to Ishad N'Ha. I took the Shroud and teleported back. So far so good.
When I approached Erathsmedor, I found two silent beings, Erathsmedor and Kol, standing in the Erathsmedor's room without taking any action. They lost their scripts obviously! Therefore, I was unable to tell Erathsmedor Elseramavin and give him the Shroud. I have to kill Erathsmedor and use the "killing the trigger triggers the action" feature of the game.
I don't know whether Erathsmedor loses its script everytime when you teleport out and back in his area or whether it loses its script only when you do that before Erathsmedor's killing Kol (the later was my case). At any rate, I recommend having the Shroud (and the Ring) in your inventory in the moment when you are entering Erathsmedor's area.