We don't need fully self-aware machines to get to that point. For example, when self-driving cars become pervasive, they'll remove a source of livelihood for a large section of human population. Driving has a low barrier to entry and can be done by most able-bodied humans irrespective of their level of acquired intelligence. This description works for most jobs that are going to be automated away.
Typically any automation problem we solve rolls out globally at a staggering rate. It puts people out of jobs faster than they can skill up. Also, social and economic mobility is externally constrained (and changes can only happens over 2 or 3 generations), and not everyone can move up even if they try. Which means automation will give rise to an increasing number of people who cannot undertake non-automatable knowledge-work, and thus become doomed to be unemployed, and leads to a self-reinforcing cycle out of which they cannot escape. This is a problem that the civilization has to confront, and our current way of thinking about economics will not work there.
The so-called 'fruit of others labour' notion is something that made most sense in the pre-industrialized era. Applying it today in its entirety without considering how much of an inter-dependent society we have become is simplistic. This is as true in technology (open-source software that powers commercial entities) as in other fields (research that builds on top of pre-existing knowledge, industrialized economies impacting global ecosystem, ..).
If we consider that each of us is beholden to the collective past of entire humanity, the idea of ownership and 'fruits of labour' becomes just a social construct. This construct nevertheless is required today and for the foreseeable future as the only practical way to divide resources. However it is a complicated and probably intractable idea, and is not at all axiomatic as you seem to make it out to be.