A few will, but most will use their newfound flexibility to shift what they work on: explore other career options, create art and culture, etc. Overall there will likely be a lot more entrepreneurship, invention, science, art, literature, and music.
It's tied into the far right's religious-based doctrine of original sin view of humanity: we are miserable evil disgusting monsters who must be beaten and cudgeled into exhibiting any form of virtue. If it weren't for life-or-death struggle we would all sit around, drink beer, play video games, and probably screw goats. It's the same mentality behind strict physical discipline of children... if you spare the rod, the kid will grow up to be lazy or a monster.
Besides, the people who would completely stop working are the lazy people nobody would want to hire in the first place. You're not losing much by taking those folks out of the work force.