So the solution is to keep a permanent underclass of people receiving only the minimal income required for life, therefore by definition being staying in poverty
You can create government guarantee jobs for anyone willing to work, lower hours, spend more, get in basic income, etc. There's a lot of options. There is no reason why anyone should be as poor as some people currently are, though. It's bad macroeconomic policy that allows unemployment right now when automation hasn't even taking over yet. There's no reason for it when there is much more resources today to distribute.
and at risk of having more children who in turn cannot get a job outside of the most menial of labor.
Hitler gave eugenics a bad name. That won't change until genetic engineering or people become more receptive of eugenic policies. In the mean time, piss-poor people will keep having kids like they always do.
Jobs have been replaced by computers and machines for over a century and it has never affected unemployment rates. People can and generally will find new lines of work if allowed to (e.g. if living in a nation where welfare doesn't pay more than employment).
A libertarian society will create unemployment. It's an egoistic model.