Assuming the following scenario:
I play a Band of Misfits or an Overlord (with the new Command type) and choose a duration card as target, which happens to be the last one of its pile (and due to the Command instruction remains there).
You're confusing the Command type with the "play it and leave it there" mechanic - a common confusion. Band of Misfits, Overlord, Captain, Necromancer, Inheritance, and Way of the Mouse all say "play the card, leaving it there". Only some of these have the Command type, and that's because of something else, namely preventing loops.
(I actually think they all should have the Command type, to make it consistent and easy to explain, but Donald thought it was better to only give it to those that needed it.)
No, I don't think I am confusing the type Command with the new instructions. In the original post, I just wanted to identify about which version of Band of Misfits I was talking. Sorry, if that was unclear, I think the misleading part was what I wrote in parenthesis (highlighted above in bold).
My point rather was: In the previous version of BoM, the instruction was: "This is that card until it leaves play" instead of "play...., leaving it there" in the newest version. Thus, I wondered what happens when an opponent gains the BoM'ed duration card from the supply before my next turn (which also happens to be the last of its pile), when I (want to) continue to play the BoM'ed duration card (and pick up set aside cards) in my next turn. In the previous version of BoM, this was not a problem, because the selected duration card is still in my playing area (along with set aside cards), and thus cannot be gained by other players before my next turn.
Edit: I just realized that already the title of this thread is misleading. Anyway, the question was intended as it has been stated here with an emphasis on "leaving it there".