Maybe they won’t and for a time they’ll live in their filth and starve. But who wants to live like that? Since time immemorial people have been finding ways to feed and clean themselves and others without notions of profit, wages, division of labor, mute compulsion of work or starve, etc. People have figured this out before and we can do so again.
Surely you clean your own house and stock your own food, if not cook it yourself? The same compulsion that drives one to clean their own homes and feed themselves will continue to exist on a societal scale even after work has been abolished.
Antiwork does not mean unpleasant tasks will disappear, rather that these will vs collectively managed in a way to maximize leisure. In the book The Dispossessed by Ursula K. Le Guin, a book that has a lot of antiwork themes, people take turns cleaning and dedicate 1 day out of 10 to take their turn doing chores in their community. Every other day they’re free to self-actualize in whatever way they see fit. There are some parts of the book that isn’t antiwork, like a machine that sometimes assigns people to only manual labor when they’d rather write, but generally the book isn’t a model for antiwork and that plot point was part of the central drama of the text.
What if people refuse to help clean or take turns doing unpleasant jobs if they are able, however minimized it has been made? In the The Dispossessed, this is mentioned. In the book, those people are treated differently, and people regard them less. Think of it if you had a roommate who is a slob. You’d be contemptuous of them. But who wants to be held in contempt? People want to be liked. The cost of these tasks is no longer “work or starve” but “help out or you’ll be disliked.”
There will be other ways to persuade. I cannot recount them all. And if they persist? Let them. It is better that a few freeloaders live than everyone live under a regime of work.