Since this question is asking "should", I think it's fine to answer with a rational but radical answer:

• People can be useful to society even if they aren't employed in our current economies. Retired people may not have jobs, but often still perform productive or necessary labor, like maintenance, artistic contributions, child care, historical preservation. When someone isn't working for money, they still often voluntarily work for society!
• I believe that, generally speaking, it's within society's best interest, even just from an economic standpoint, to support these people even if they aren't formally employable.
• Looking at most capitalist countries, overproduction is normal. Usable property remains empty just because an owner wants more money for their investment. Perfectly edible food is systematically thrown in bins rather than given to hungry people for free, or rejected by stores because it doesn't look perfect (like an oddly shaped carrot). Clothes are thrown out once they're "unfashionable".

We have all the resources needed to support everyone, and it wouldn't take much extra effort from a determined government to get those resources where they need to go. There's no reason why unemployed people should be left to starve and freeze simply because they don't have enough income. In our society, the scarcity of basic needs is artificial ('artificial scarcity').

Automation is seen as a bad thing, a threat, because workers in society are threatened with starvation if they don't have the income needed for food, shelter, medicine and perhaps basic luxuries. But if our political economy were first-and-foremost based around society's needs instead of profiting, and therefore we used our modern technology to automate the production of these basic needs and distribute them, then suddenly automation would mean free time and easier labor!