maybe it wouldn't be so much "Soul" as it is "Design Force", akin to what happened in DivineZ.
so sum it up. Each of the participants have a mark on them that is held together via Design Force. Using that Design Force, they are able to "Ride" onto Cray as themselves, but once defeated, they dissipate and return to Earth.
and of course Aichi's going against that rule by using Psyquallia.
So next fight is going to be a Vyrgilla vs. Alfred fight...
...makes me wonder when they'll come out with regular encounter cards for Gallatin and Soul Saver Dragon.