I would assume that the Global Establishment want to take the collapse just to that point where they have achieved the maximum power; by means of their currently-favoured mechanisms of omni-surveillance, total control and the domination of a single bureaucracy.
But such would necessarily be a high-tech highly-organised modern dystopia; whereas if things go much further in the direction of collapse; high-tech and organisation will be among the first casualties - and likely impossible to restore.
This is an aspect yet to emerge, yet to become clear. Will this global collapse stop short of destroying the infrastructure of global governance? Or will it continue beyond that point? Is this of the nature of an intended re-set, or is it an all-consuming, apocalypic outcome that is planned? Re-boot or Revelations?
It looks as if those in ultimate control (that is, the demonic entities who influence, sometimes control, the most powerful humans engineering the totalitarian takeover) may well intend to take this collapse a great deal further than would benefit the Global Establishment... Into realms where the vast apparatus of world trade, economic specialisation and coordination, bureaucracy and the mass media - and the vast leftist ideologies of equality, antiracism, pseudo-environmentalism and the sexual revolution - all collapse into universal chaos.
If matters continue to the point where the Global Establishment cannot govern - because the tools of governance have been destroyed by the same collapse that (so they believed) would lead them to absolute power; then this may turn-out to be a situation in which the Global Establishment have been demonically deceived, along with the masses.
On the whole this latter scenario seems likely: that the Global Establishment will at some point realise that they have been tricked; and are not going to be raised up as total rulers of the world; but instead reduced to the same level as the masses of the world.
After all, the demonic spritits are not 'on the side of' any human beings, indeed ultimately each is only out for himself; and such double-crossing deceptions are, apparently, their favourite activity of all.
So when evil is triumphant, we should Not expect to see the emergence of 'a new stability' - but wave after wave of increasing chaos with no end-point sought or attainable; as evil turn-upon evil in sub-dividing groups; until it is each for himself, here and now. And ultimately a single winner, presumably Satan - and then (since he hates all of creation) his own suicide.
(Meanwhile, those who have chosen Heaven will look on all this with sorrow; but with other and greater matters of loving creation as their primary concern.)