The Subliminal is rather like the Inner Being; in fact it includes the Inner Being. However it also seems similar to the Middle Unconscious of Assagioli (no. 2 in the "egg diagram")
The following summary is from Growth Online [ref Theory of Creation - Involution and Evolution]:
The following passage is from Sri Aurobindo's The Life Divine (10th ed.), , Chapter XXIII, The Double Soul in Man.
"...as we now know by psychological observation and experiment that the subliminal mind receives and remembers all those touches of things which the surface mind ignores, so also we shall find that the subliminal soul responds to the rasa, or essence in experience, of these things which the surface desire-soul rejects by distaste and refusal or ignores by neutral unacceptance. Self-knowledge is impossible unless we go behind our surface existence, which is a mere result of selective outer experiences, an imperfect sounding-board or a hasty, incompetent and fragmentary translation of a little out of the much that we are, -- unless we go behind this and send down our plummet into the subconscient and open ourself to the superconscient so as to know their relation to our surface being.
For between these three things our existence moves and finds in them its totality.
The superconscient in us is one with the self and soul of the world and is not governed by any phenomenal diversity; it possesses therefore the truth of things and the delight of things in their plenitude.
The subconscient, so called note, in that luminous head of itself which we call the subliminal, is, on the contrary, not a true possessor but an instrument of experience; it is not practically one with the soul and self of the world, but it is open to it through its world-experience.
The subliminal soul is conscious inwardly of the rasa of things and has an equal delight in all contacts; it is conscious also of the values and standards of the surface desire-soul and receives on its own surface corresponding touches of pleasure, pain and indifference, but takes an equal delight in all.
In other words, our real soul withintakes joy of all its experiences,
gathers from them strength, pleasure and knowledge,
grows by them in its store and its plenty.
It is this real soul in us which compels the shrinking desire-mindto bear and even to seek and find a pleasure in what is painful to it,And this it does because it is impelled by the universal to develop itself by all kinds of experience so as to grow in Nature.
to reject what is pleasant to it,
to modify or even reverse its values,
to equalise things in indifference
or to equalise them in joy, the joy of the variety of existence.
Otherwise, if we lived only by the surface desire-soul, we could no more change or advance than the plant or stone in whose immobility or in whose routine of existence, because life is not superficially conscious, the secret soul of things has as yet no instrument by which it can rescue the life out of the fixed and narrow gamut into which it is born. The desire-soul left to itself would circle in the same grooves for ever. "
footnote by Sri Aurobindo:
"The real subconscious is a nether diminished consciousness close to the Inconscient; the subliminal is a consciousness larger than our surface existence. But both belong to the inner realm of our being of which our surface is unaware, so both are jumbled together in our common conception and parlance."back
The desire-soul in fact would seem to resemble what the Christian theosophical-esotericist Ann Ree Colton calls the Undersoul, the realm of ego and "maya" which contains the self-perpetuating lower samskaric tendencies