This would have to be in a different industry though, no? Inherently the point of automation is to shrink the amount of labor required to do a task. So as to your comment and in my example of customer service, employees laid off from company A would need to acquire technical skills to manage the new automation in that industry (likely that company B has already, or will adopt), or move to a different industry completely.
The problem I see is that everyone is automating though. Or is it assumed that enough tasks can't be automated to actually effect unemployment?