For instance, in the West Village neighborhood of Detroit, there is now the Red Hook, a cafe started by Sandi Heaselgrave. Ms. Heaselgrave, a photographer, moved to Williamsburg from Detroit directly out of art school in 1998, only to find herself moving back with her husband and son five years ago. And on the shelves of most stores are jars of McClure’s Pickles, a “Brooklyn/Detroit” company that is selling its quickly expanding line nationally.

But while real estate is cheap and available through agents and public auction sites, particularly for those willing to navigate a complicated system, there are also hidden costs to the purchase price: back taxes, old water bills and, for the most dilapidated properties, financing a complete renovation from electricity and plumbing to a new roof and foundation.

“I estimate it costs $100 a square foot to rehab an empty house here, and that is without doing anything very upscale,” said Amy Haimerl, a former Red Hook resident who moved to Detroit in 2013 after purchasing a 3,000-square-foot house for $35,000. Since then, she and her husband have spent about $400,000 fixing it up, documenting the refurbishment on her website — though they have not cut corners, putting in a gourmet kitchen and installing old moldings from an abandoned church.

Others, like the community activist and artist Halima Cassells, are experimenting with more frugal ways to fix up a previously abandoned building. Ms. Cassells, who during her six years in Brooklyn moved seven times, is now back in her native Detroit and the proud owner of a two-family home she recently bought for just $3,100, including back taxes.

As an extension of the “free-market movement” she began here, in which community members trade items they no longer need at regularly organized swaps, she has started a “builders’ club.” In the club, those who help labor on the house’s restoration, which she is documenting in a blog, will in return be given space to work in what she hopes will become a rotating workshop for community projects and artists.

“One thing anyone moving here needs to know is you have to come into Detroit respecting the people who have been living here through all the city’s struggles,” Ms. Cassells said.