It's a reasonable question, but I think automation is ultimately just going to mean that there is less work overall that needs to be done. This means that overall, people are going to be working less. For instance, it might become standard for people to only work three or four days per week.
This shouldn't really be a bad thing, in fact for many individuals, extra free time would be a good thing. In reality, though, there are problems presented by this. A lot of people would not be able to sustain the pay cut from working fewer days in a week, but since the reduction in staffing costs is the greatest incentive for businesses to automate, they won't be in a hurry to pay more to make up for this. Another problem is that automation doesn't generally gradually reduce everyone's workload at the same rate. It wipes out the need for entire workforces while leaving others relatively untouched.
Finding new jobs for displaced people solves the problem temporarily, but eventually we will run out of work that needs to be done. What then?
So there are two options. Either society shifts away from the idea that every healthy adult works a 5 day week, or equivalent, to sustain themselves and their family. Or automation is disincentivised to keep people in work. Neither of those will be without their disadvantages, but I think the former is the lesser evil in the long term, even if the latter is more popular in the short term (which I'd certainly expect it to be among conservatives/traditionalists).