In the Dawnguard questline, Serana offers to do a partial soul trap on the Dragonborn. But being a dragonborn, he/she has the soul of a dragon. Can a dragon soul be fully contained in a soul gem? Serana managed to trap a portion of the Dragonborn’s soul, but I’m not aware of anyone trying to trap an entire dragon soul.
I assume that dragons have 100% soul-trap resistance, so that casting Soul Trap on one would have no effect. If that’s all it took to trap a dragon soul, someone might have done it when the dragons returned to Skyrim. (Enough city guards could kill a weak dragon, even if you don’t help them.) Still, the Dragonborn apparently does not have soul-trap resistance, since Serana was able to cast a partial soul trap on him.
What happens if someone casts Soul Trap on a dragonborn? Did anyone ever try to soul-trap someone in Tiber Septim’s line, for example?
(From browsing UESP, it seems that enchanting was first practiced in the First Era, while the Dragon War was earlier, in the Merethic Era. So probably no one tried to soul-trap a dragon during the Dragon War, but the resurrected dragons ought to be fair game for soul-trapping, if it’s possible to accomplish.)