I think there's a couple different approaches right now. One says let the kid live at home while he goes to college or even just because he's unemployed (or unemployable). This may have limits, like "you need to be in college" or "you need to prove you're sending good resumes to legitimate job opportunities".
Another says the kid needs to move out as soon as he's 18 because he's an adult now. This may have wiggle room, like "you can stay home but you need to pay rent" or "stay until you're 19 or 20 but there's going to come a day when you will be kicked out."
I've also seen an approach where the parent supplies financial support in exchange for fealty and forgiveness for being a shitty parent when the kid was growing up. It's a strange kind of clannish cronyism.
In the stereotypically American culture it's uncommon for extended families to live together, although this provides a lot of security and support. Frequently families drift far apart geographically. I've seen family members fling themselves to some other state without preparation, leaving steady jobs and good housing, only to return months later after having absolutely failed in the new region.
That said, recent immigrants and immigrants who have maintained their cultural distinctiveness despite living in the middle of more typical American living styles, will band together with perhaps a dozen or more people in a dwelling that's legally habitable for no more than six. In my state, the terms of a lease generally state that anyone living there must be on the lease. So you have a couple with one or two children rent a three-bedroom apartment, and then later you find out they invited the aunt and uncle, three cousins, a felon who just got out of jail, and five or six miscellaneous children. This is not an exaggeration at all. One family had a sectional couch in their living room that ran along all the walls of the living room, walling in the sliding glass door, because that many people would regularly need to sit in the room at once.
In my imagination there's a mythical Italian or French family with a beautiful stucco house and a garden, and four generations of the family eat dinners together on a sun-drenched patio with vine-laden trellises shading them. The adults all work, the grandparents relax and mind the children, and because they share burdens and joys they're relatively wealthy and happy.
In America many people labor away at two jobs, alone, or a couple with several kids, until they die of poverty at 60.