The term in "Worst Case" planning is "Managed Die-Back". It/s considered an "extreme" way of correcting "overshoot" conditions.

There were studies done in the 80's, as part of the "Star Wars" research, on the use of satellite deployed kinetic energy weapons for this purpose. As effective as a nuke, but without the nasty radioactive fallout.

It would be a desperation move by the Elites. Abandoning the cities and using the military infrastructure to try to retain control of the rural populations would be very dicey.