The soul is something remarkable in human conception. Aristotle would say that the soul was the actual form of the body, that it was one in the same with the body and could not be separated from it since it possessed its own inherent behaviors. And this was not only applied to humans, but to trees, daisies, dogs, cats, and the noble platypus, natures D-student. Absolutely fascinating notion though, especially at this point in intellectual history since you have this genuine attempt to mesh a burgeoning scientific inclination to abstract principles. Aristotle would call this the pneuma, the breath of the cosmos that, at least in my opinion, gave animation to the deeper ontological designs of the human. Even Descartes commented on this in the form of the spiritus
, from the stoic conceptions of this grand immaterial "something" that was both the causal form of the cosmos and the reason why Timmy grew one inch taller this year, why Timmy hates cheese sticks, or why Timmy believes that spinach is bad.
But Descartes, Plato, and most everyone else and their mom would say that the soul is an immaterial part of a body that shared a connection but was not necessarily bound to it permanently. Saint Thomas Aquinas even mentioned that in the corporeal realm, the unification of body and soul was the foremost natural way. But even with the fact that the soul may have a relationship with the body in the case of Descartes, the soul is substantial. It is in the respect of tangibility that the issue prevails I suppose in this case.
Could someone own my soul? Depends on your conception of a soul. If you were to believe, for example, that the soul shares only a passing relationship with the body, then perhaps not. However, even in this respect, that is not to say that there is some entity which could exist and have some bond with my soul. In such a case, I don't know, but it would be wise for me to think that it could happen. Why? Because if I find out, when I do find out eventually, that there is something that has a bond with my soul, I acknowledge beforehand that it is so. If there is not something, I do not lose anything in affirming that bond, only if I deny that bond and find out that the bond does exist.
In many ways then, ownership of the soul is either absolute in the terms of this bond that we don't know we have or non-existent. Then, a sort of implied ownership, with nothing explicitly stating that "x owns my soul." And this is to say that someone on earth in my corporeal realm could most likely not own my soul, unless they had some way to tangibly say "here is your soul, check it out." But if anything, there are still major issues with ownership of physical certainty. Do I really own my body, and if so, am I not subject to this or that law. Do I have ownership of my land ad astra