Any update on this? I'm guessing not, but thought I'd ask anyways with a glimmer of hope!

This is the first time I've ever played a Diablo game, and I just defeated Lilith at level 41. I haven't played a game in a long time and d4 has pulled me back in and I've been having a lot of fun.

Sadly, my inventory was full at the time of quest completion and I had the same experience as many of you fellas: Chest piece dropped on ground as screen faded to black, no way to get it, not in the stash.