How would libertarianism deal with full automation?

It’s a very real possibility that AI and machines will become so advanced and cheap in the future that they can replace 99%+ of jobs humans do, and that any new jobs created by automation can just as easily be filled by more automation. Maybe it will take 50, 100, or 500 years but it very well could happen eventually. How would a libertarian society go about dealing with 99% unemployment as a result of this? I’m not a Marxist, but I think eventually Marx could very well be proven right in the end. I can’t imagine any good solution to this short of collective ownership of industry and universal basic income distributed equally among the population.