In the extreme scenario you mention, we have effectively infinite labor. Provided we also have effectively infinite energy and resources (which is entirely feasible or only a matter of time if technology is that advanced), the value of all three of those things (labor+energy+materials) drops to zero.
That means we won't have to worry about employment. It will be an outdated concept.
But in the mean time, we also have nothing worry about, for the reasons I mentioned.
Problem is, the price of the nonlabor factors will never actually drop to zero. Energy and materials are basically things you pull out of the ground, and there's always going to be rent-seeking on natural resources.
That means we won't have to worry about employment. It will be an outdated concept.
But in the mean time, we also have nothing worry about, for the reasons I mentioned.