Possibly Kairi had lost her soul, as well, so had no remaining animating force
Heartless could be kind of like some kinds of Japanese ghosts, where the heart or animating emotion remains, leaving a shadow of the person. Ansem, after all, seems to have just one animating drive (to open the door) much like those kinds of ghosts have one purpose (to finish what they died for, but always trying to do that one thing). So, sundered hearts could be the emotion/purpose/instinct of a person (they're animating drive)
Then souls, like in most philisophical thought, could be the freewill, reasoning, and memories of a person. Memories must almost certainly be included, since Chain of Memories seemed to be messing with the soul. However, it is possible memories are in the heart, judging by some quotes, and the fact that the Order mems seem to not remember their past, which would also help with BHK being a Nobody, but Ansem, Sora, Kairi do (right?).
Then, bodies would just be the vessel that manifests these forces and protects them: this is why heartless die so easy, since the heart is both trying to manifest ITSELF (which leads to it being ineffeiceint in all 3 tasks, to the point of not completing heart function almost at all) and trying to carry out its purpose. Thus, its "shields" are down.
Or Sora and BHK are jsut Siamese twins that we're surgically seperated at birth. Who really knows?
I thought a Nobody was formed when a person with a strong heart became a Heartless, and yet did NOT lose their heart... like Ansem. In that definition, SORA would be a Nobody, too, wouldn't he? If Sora's the Nobody, then how could the BHK be a Nobody?