Controlled? I doubt it will go that smoothly. It’s being done on purpose, but nobody is in control.
Think of a scenario akin to Biden’s/ US withdrawal from Afghanistan.
Yes, anyone thinking they will maintain control through something like this is absolutely delusional. It would bring a huge portion of the population to a place where civilization literally has nothing to offer them, and that includes the military.
The guy who can feed people would gain their allegiance, not an abstract leader thousands of miles away. This is why it hasn’t been so long ago that the usual system of government was feudalism.
And if they actually succeed in drastically reducing the human population they are going to find that everyone’s standard of living is reduced to something very similar to what it was when the population was last at that level.
Many technologies require a large enough population to support a lot of specialization. That includes agricultural technology. One thing it would absolutely bring to an end is the legions of useless people producing nothing of value.