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If they are anywhere but your territory when it comes time to "exchange back," they stay yours permanently. So you could use Stalks of Flax to grab some doods, then set them aside with Standing in the Gap or The Lord Fights for You for >2 turns, then they're yours. But beware, your opponent can do the same with the characters you gave him.
Cards are set aside in their owners’ respective set-aside areas
So if I set aside a Flax'd hero in Kereth Ravine, it gets removed from Kereth Ravine and just kind of wanders over to my opponent's Set-Aside area? I'd say that doesn't sound right, and that section (like most of the REG) is flawed and incorrect.
During the turns that our heros are exchanged, can I use my good set-aside enhancement on those temporary heros?