Out of business, but not necessarily out of existence.
If there is really nothing for humans to do, whoever has control over (not necessarily ownership of) enough robots and AI to directly maintain and grow their collection of robots and AI, has something functionally equivalent to a breeding population of the stuff. (If they can't make more of themselves and humans made the initial batch, then that's a job humans can do so the initial condition has not been reached).
None of this helps people figure out how to look after their own interests in the meantime. The rest of society may carry on as today without AI, akin to the Amish if we're lucky (rejecting further developments unless good for us) or like Pol Pot if we're unlucky (reject anything that nerds like because nerds liked AI and everything breaks down).
On the other hand, the institutions may simply fail to handle reality, like in the Great Depression.
Out of business, but not necessarily out of existence.
If there is really nothing for humans to do, whoever has control over (not necessarily ownership of) enough robots and AI to directly maintain and grow their collection of robots and AI, has something functionally equivalent to a breeding population of the stuff. (If they can't make more of themselves and humans made the initial batch, then that's a job humans can do so the initial condition has not been reached).
None of this helps people figure out how to look after their own interests in the meantime. The rest of society may carry on as today without AI, akin to the Amish if we're lucky (rejecting further developments unless good for us) or like Pol Pot if we're unlucky (reject anything that nerds like because nerds liked AI and everything breaks down).
On the other hand, the institutions may simply fail to handle reality, like in the Great Depression.