For dream, perhaps a collective unconscious dreamscape 'extruded' outside the world, such that they can exceed the limits of reality and draw inspiration from without. I got one such structure at hand.
Take Dream, a realm that metaphysically exists simultaneously inside every thinking being's head and as a multilayered plane. Dream's geography is based on metaphor and relations, people who think alike, or have strong emotions towards each other are connected by paths and tunnels. Those of common faith generally form a nexus in their dreamscapes. It does have some correspondence to real places, if only because many people dream of real places and thus are connected to the common concept-space of that location(that is to say, someone who lives in New York is going to be mentally linked to the concept space of New York).
Each being exists as a blob of thought, its surface hard and difficult to penetrate while awake and focused, liquid and permeable when dreaming. When dreaming, it expands and flows to touch other minds and also the larger Dream. Each such mind-bubble is itself a layered demiplane, its contents the dreamer's mind and imagination, with the outermost layer consisting mostly of imagination and dreaming, the middle of memories and attachments, the core of personality and motives. Most of the time, only the outermost touch, imagination leaking between dreams.
When dreamers wake however, their minds withdraw back into their shells, and sometimes things get left behind. Sometimes creatures, sometimes thoughts, emotions or entire scenes and locations. This detritus forms the 'main' dreamscape, particularly for places of significance common to many people. These debris fade over time, unless they gain reality or reassertion in some way, so those creatures tend to invade dreams, to reinforce their own existence.
When a dreamer dies however, the mind blob grows brittle and shatters, filling Dream with what he used to be. Most tend to fade unnoticed, but some of these become strong loci for many minds to link to.
Now as to how this relates to the Far Realm, when a dream pierces too far outside of the protection of shared thought, dreaming of things beyond reality, it opens a vulnerability, and things Outside can influence and take the form of things of Dream, and from there, gain reality and leave Dream to ravage the world, or simply feast of reality in these minds.