That role, and that idea, had something to do with the words inscribed on a plaque at the foot of the Statue of Liberty: “Give me your tired, your poor / Your huddled masses yearning to breathe free, / The wretched refuse of your teeming shore.” The lines were about foreign immigration, but they spoke equally to migrants from other American places, who arrived simply with the longing to become some unexpressed incarnation of themselves.

As E.B. White memorably wrote, “Commuters give the city its tidal restlessness, natives give it solidity and continuity, but the settlers give it passion.” That settler might be “a farmer arriving from a small town in Mississippi to escape the indignity of being observed by her neighbors, or a boy arriving from the Corn Belt with a manuscript in his suitcase and a pain in his heart.”

But is New York still a good place for the settler whose achievements remain ahead of her?

A few years ago, Patti Smith, the musician and author, who came to New York in 1967 with some of the fervor that Mr. White wrote of, advised aspiring Patti Smiths to try somewhere cheaper and easier. “New York has closed itself off to the young and the struggling,” she told an interviewer. “But there are other cities: Detroit, Poughkeepsie. New York City has been taken away from you. So my advice is: Find a new city.”

And, indeed, many prominent people who want to fix Detroit — and New Orleans and Pittsburgh, among other places — see in a changing New York their great opportunity. What those cities may lack in security and public services, they make up for with the opportunity to crash with a bunch of friends in a $500-a-month house and pursue creative work of the sort that takes time to be recognized and financed.

In Patti Smith’s day, New York offered that, too. No longer. A fair indication of where things stand may be the New York television show of the moment, HBO’s “Girls.” A show about flailing, post-collegiate millennials, it has a cast that in real life reflects the coming of a New York whose function is to help successful people transmit their advantages down the genetic line rather than discover new successes from obscurity or even Queens.