As for Sartre, since
@Gnomon references him, yes, Consciousness is supported by a Being which is not itself. But contra Sartre, that Being is the Organic Being, the human animal.
What Consciousness is, is the system of autonomously moving images which displaces the Organic aware-ing of that Being, with the former’s constructions, empty of Real Being, and fleeting, Fiction.
The Dialectic that Sartre observed goes beyond Subject and Object, Self and Other. Like Freud, Sartre was astute enough to observe a Dialectical dynamic to Consciousness, but fixated on the most obvious Dialectic accessible to one in pursuit of an existential or phenomenological Ontology: subject/object (just as for Freud, in pursuit of Neuroses, the Sexual Conflicts were most manifest).
But dialectic is not limited, in Consciousness, to Self and Other. All of Mind moves through a dialectic; Signifiers autonomously competing to be heard, only surfacing at the arrangement most fitting for that specific locus in an individual Mind, and the locus of that Mind in History, or Universal Mind.
Even when my Body’s vision (sensation) is directed at a mundane cup; it does not “see” the Real “object,” like an equally intelligent animal might see; or, rather, it does, but there is no “object,” only see-ing and what Natural response see-ing might trigger. But with Mind, too quickly for that see-ing to be organically felt and responded to by that Real Body in aware-ing, Mind has already begun its Dialectic: Signifiers compete, and the Signifier arrangements most functional, for a given locus, surface to the aware-ing, displacing the Real Organic aware-ing with the "text", and triggering, à la Classical Conditioning, the Body to feel and or act in response to that fiction (all the while receiving those Signifiers in Narrative form, believed to be experience.).
And, only following that process, not Real, not disclosing itself to us as Real Being, but fleeting, and fictional, do I perceive that Signifier chain which won the Dialectic Dance and surfaced to Body, preassembled with belief, as that commonly shared object we call “cup.”
What is the human condition? Shit that just happens. But the point that Heidegger, Sartre, Arendt and so on are desperate to make is, ironically, right in front of our noses. We
are authentic beings, not when we construct authenticity, or reflect upon what it is to be the Being of beings, or when we allow Being to disclose itself in authentic choices etc. All those things are sincerely admirable ways to follow the Narrative, just like Altruism might be, or for some, heroic sacrifice. They feed History, and thus inevitably, all of Human Consciousness (to wit, you and I). But what's already in front of our noses is we are authentic Beings, our Body is. To be that authentic Being, just be. If any details need be provided, it would be: breathe, eat, reproduce.
But, trapped in our Narrative world, we hate that idea and end up constructing bullshit out of Dialectic. And believing it. Like this.