If the eye were an animal, then vision would be its soul.
De Anima, Bk. II c. 1
Aristotle picks an organ with a single function. Picking “mouth” gives us not the single act of vision but a whole class of actions, e.g. of chewing, breathing, kissing and conversing, and this group of actions does not enjoy a single name. Maybe in honor of Aristotle’s entelikia, and with an eye to making an adjective, we could coin a suffix -elic to describe the group. So chewing, breathing, etc. are all mouthelic; just as grabbing, punching, handling, pinching etc. are all handelic. If the throat were an animal, its soul would be throatelic.
On this account, the human soul is the humanelic. And so “soul” adds to “human being” just what “mouthelic” adds to “mouth”, i.e. it adds a shift from considering the thing as just some thing “there” to considering it as the (obviously) unified source of all the mouth can do. Soul is not opposed to body but to the thing other than a source of action. Clearly there is some overlap between body and “what is other than a source of action”, since body is characterized chiefly by its inertia (inactivity), but merely being physical or extended isn’t what one wants to target as the opposite of soul. Soul is opposed to “stuff” or whatever could be one thing or another. It is precisely this that makes it a form of matter anima forma corporis.
And so we see first that the soul/body opposition, and the supposed opposition of them as invisible/visible is misleading. Is that which unifies chewing, kissing, and speaking invisible? Perhaps as a unity, but anyone can visualize a mouth. But if mouth were an animal, it is just this unity (what we called the mouthelic) that is its soul.
The humanelic is invisible in certain ways, though not as soul but in ways that everyone seems to agree on. We all recognize that there is a danger in mixing up the epistemic/logical and ontological/ physical worlds, or with “confusing the map with the territory”, which means we recognize that the conceptual and moral world plays by different rules than the physical one. In this sense the humanelic must be at least partially characterized as non-physical. If these humanelic elements exist, then asking whether they can die, decompose, or corrupt is like asking if an oak tree can be modus tolens or a field equation can be prudent. This doesn’t quite address the problem of “continued consciousness” (which is how immortality is usually understood), but it helps to position the question for a further inquiry.