If the answer is a mass die-back of the bulk of the population who constituted the now economically unnecessary labour class, where will the genetic diversity come from to prevent the handful of owning families (and the retinues of explosive-collared servants they retained for tasks that can’t be automated) from speedrunning Habsburg Syndrome? They’d need some kind of biodiversity preserve in which sufficiently large numbers of people are kept alive to provide suitable candidates for outbreeding, and some means of ensuring that this captive population never poses a threat.