If 99% of people are living effectively outside the economy, those things they could have would too have to be entirely provided by AI (including the mining of materials and building of robots by other robots capable of doing that work). For ordinary people, if money becomes useless why would they take a job at building a shelter or providing private security? They might as well be offering monopoly money

EDIT: An obvious response to this is that workers could be paid in food, rather than money, but that just kicks the can down the road. Who is making the food? The rich would still need to eat, so this would have to be done anyway, but the supply lines needed for food production are far more complex than private security or construction, if you've got that automated you could certainly automate the rest of it without needing workers.