They actually directly refer to Dreamer Reborn near the end.

Dreamer Reborn is one of my favorite UT fanarts.

The point was to try to reconcile the canon with fanart like Dreamer Reborn, using the "meta" nature of the game. That way it gets rid of the cognitive dissonance.

TL:DR version.

The game is meta and aware that we, the player, are interecting with characters in the game world.
By quitting after the game after the pacifist route as suggested by Flowey, the story thus continues outside the game, since we're a part of it.
Through blogs, art and literature that follow where Asriel is saved, we saved him by pulling his character out of the game.
He lives on and has his life because we used our DETERMINATION - aka real life ailities - to create a reality where he was saved.

I endorse this.

Yes. :)

Thanks for the tl;dr version, hehe.

To be fair I think Asriel was partly saved. Through his actions and absorbing all those souls to revert back to his original self before becoming a flower and then later turning back and giving you a speech as Flowey to not reset the world. This is one of the nicer things if not the nicest thing he has done AS Flowey. I think it's very possible when freeing the souls he had kept a part of his parent's souls. Which is the normal way boss monsters progress in the aging process. Though if you want a real canon way to save Asriel? Get Sans' time machine to work, go back and stop Chara from ever reaching the underground. Little bastard ruined a majority of lives by existing.

Sure, that works too. :)

Flowey at the end is Asriel minus Chara so he's not insane or evil now.
It's also Asriel minus the fucked up mindset resetting the world and killing people gave him.

If you d take the game's ending at face value, Asriel is now a flower again but there's no more resets, he's not insane or evil, maybe not even alone.
And many ways to restore him fully exist, maybe in the future...

Unfortunately for things to be set in motion all of that needs to happen.
But a story at Archive of our own presented the idea of going back to the moment that Asriel died to absorb his soul before it shatters. Of course that chapter, which is the latest also left Frisk confronting Chara.

On that note, here is a theory. What if the first child was had already sold their soul before going to the underground.