Zelazny gives us nothing much to work with regarding the surrounding shadows of the Courts of Chaos. So I use it to support the themes of the Amber universe and my own political interpretation of the Courts that Zelazny does give us.
But collecting the interesting or valuable ones, the gems dug from the dross are worthwhile to some Chaos Houses.
So IMC, the Black Zone is made up of the select shadows that have been surgically removed from wherever they originally were found and transplanted to nourish under the watchful patronage of a particular House of Chaos. Keeping these shadows vibrant under near-Abyss conditions is not easy, but it has rewards, too.
But the desires and needs of the Black Zone are hardly the concern of Thelbane, or even a majority of the Houses. There are no treaties or mutual-regard pacts as might be expected by those diplomats of the Golden Circle. The Black Zone is essentially a buffer of captured states.
One might almost see them as occupied territories with oppressed populations—but the people of each shadow within the Black Zone would have very different viewpoints on that.