The Cage is not a place. It is a thing.

It is alive, in the most drawn out, cut apart, defiled sense of the word.

It is not undead.

It is not sentient.

It is "alive".

It is aware of nothing, but everything it needs. It is not malicious, but it causes pain as it's general, default setting, it gains knowledge, but does not technically learn, does not use it outside of where it was deemed required. It most senses, it lacked creativity. More basically, it lacked a soul, or a Grace, or anything like it. It was not empty, but rather, had no place designated for such a thing. It was complete, and it had all it needed for it's sole purpose.

For it was built to house an archangel, and the only way to keep Lucifer from escaping was to tear at his being, distract him away from any attempts. It focused upon him and completed this task. It worked at his very essence.

Angels do not have souls.

But they have Grace.

And it functions in much the same ways.

The demons, long, long ago, had chipped at the Cage - when they knew where he was housed, before the cage made them lose the knowledge, for it can make unawareness of others, inflict it's own emptiness of thought and memory as well as any trauma - attempting to free their Prince.

They found that it did not change.

It is not well to say that the missing parts grew back, for that seems organic, and the Cage was not. It simply was. Automatic, unaffected by their peeling and hacking at the walls, it simply was new again. It did not regenerate, did not reincarnate. It was for a second a crack, a wound, a dent, and then it was gone. Should someone attempt to stick their arms in and keep ripping away, their arms would be forced out. Not shoved out, but squeezed out. As if suddenly the space they took was already occupied. The screams as soul was rendered and pressed out like pulp and splintered bone were foul and wretched, the first that true echoed in Hell. It was how they came to realize that the shards among their feet could cut a soul and maim it - though impermanently, in it's own way.

A soul is different from Grace, but while the Cage shredded minutely at Grace, and blackened it, after several thousand years (for Grace, but souls, not as resilient, not created to power Warriors Of God, were infinitely weaker in that regard), just as souls, tortured on end for decades, began to twist.

The shards could not cut away or inherently damage a soul - rather, emotional and painful procedures were adopted by the demons to make it easier for the Cage pieces to do their work - they could imperfectly warp the soul, the Grace, like forcing a ceramic to change after it was already placed in the kiln. It was slow, and irksome, but it could be done.

For their Prince it was an unavoidable, highly undesirable side effect of his prison, his Grace not beat upon, not bruised, but pushed at, like gravity, constantly pressed at, undoing perceived perfection. They, instead sought to bolster their ranks so that He may have had a glorious army upon His return. He would have truly hated them if He didn't care about human souls.

Even He could admit the souls were things of beauty (plain, next to grace), but when brightly new and untarnished, He could admit they were as most of His Father's creations had been - flawless.

Humans, themselves, once that soul matured and that weak body was added, were unsavory and nauseating. In part it was the losing of it's luster, the dimming of the soul that Lucifer found so abhorrent. A beautiful thing had been lessened, He believed, made into something violent and cruel and weak. For all the loss of innocence, it was still childish and unworthy of a place above His love for His Father.
He could not watch them and look upon His Father and find them to be more.

He could not.

it was inconceivable.

The Cage was meant to know these things, and these things did it use. It drank up his sufferings and poured them back in, changing his Grace and therefore changing Him. He became Satan, though he did not accept the name in his Grace. It remembered Lucifer, for it was Grace, and could not become part of something other than it's Heavenly calling.

The Cage absorbed all his pains, and the pains that came too close to it's "walls" (it remembered the first demon to try to halt the return of it's completion, the severe agony that pulsated it's being and kept it deep in it's "memory", where it was never returned to, never used. ).
It could put all the pain it knew of and put it in a vault and never would it put any of that pain upon Lucifer. He realized it didn't know to. It didn't know that they could be used. Or rather, it was not required. There was no reason to, so, like a kleptomaniac, it took all those memories of pain and kept them, for absolutely no purpose. The memories were not dissected, not analyzed, not learned from.
They simply were.

When Sam dragged Lucifer and Michael, and even Adam back into the Cage, Lucifer despaired. He had not done so in a very long time, but he remembered the absence of color that permeated this place, and thought Sam had not understood what he was sacrificing himself for.