Though there's theories about the population count plateauing soon, currently humans overall still mostly have an overpopulation problem, so I'd imagine a lot of people would say "awesome!" and continue to go on their lives exploiting the population cap. Either as a freebie fix to actual overpopulation, or people best poised to profit in a zero-sum game (assuming the cap applies at a uniform rate across everyone, countries with poorer healthcare and higher mortality rates would start to be edged out by countries with better health care).