I don't think it's ever spelled out, other than it can happen like in the case of that one portion of Arcadia that fell into Mechanus because everyone there was so much more LN than LG. From the sound of it, it was a literal detachment of Arcadia that moved into another plane. As such I imagine, it would come with a suitable change in atmosphere and environment.
I imagine a Silent Hill transition from the "Ethereal" plane where it is to "Hell" where it's other half is. Or possibly more subtle than that.
For material to abyss, I imagine there's a big earthquake which breaks off a chunk of land, forming a literal island as it falls into a deep void. It ends up floating somewhere in the abyss, still with gravity and oxygen as planes are wont to defy logic like that, and things upon it take a turn for the CE, probably warping stuff, causing chaos with the elements of the environment you have, and basically demonifying everything and everyone up to your degree of showiness. On the material, it probably leaves a bit pit or scar where it happened with appropriate abyssal-themed changes, but not as a global effect and non-permanent (aka a tower which remains in the material is warped and distorted, but may be knocked down and rebuilt normal with no ill effect).
