This assumption has been wrong, and will continue to be wrong for the rest of human history.
First off, because there will always be more things that people want.
Second, because robots, in economic terminology, are tools, not consumers. They produce goods at the behest of who owns them, but they do not create economic demand, so effectively they add value to the economy, but do not absorb any of the value created.
As with literally every other part of human history where automation and tools have made production more efficient, new jobs will come into existence, because people who have more effective purchasing power because the goods they buy have become cheaper due to automation making costs lower, will spend that money on other things instead. Those other things will need to be made, and thus more jobs will come into existence, etc, etc.
What we see again and again in the post-industrialization world, is that the surefire way to create high unemployment rates, is for the government to mess with markets, especially labor markets, to try to 'fix' things. Then after high unemployment comes high crime, which then drives up costs, which spirals into destroyed cities and ghettos.
The world is rife with examples of what I've described above, and has exactly zero examples of what the 'automation will result in permanent unemployment' people claim will force us to use UBI/BLS to keep society going.