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Lillie Walsh Dudley and Andy Dudley wanted to be homeowners. The couple, who have a 5-year-old son, had been renting in South Slope since 2014. They began looking for something to buy about three years ago.

“Even though we’re not rolling in money, we had a little bit of savings,” said Ms. Dudley, 41, who works in book publishing, as does Mr. Dudley, 45. Still, not enough to buy in Brooklyn. “Anything we could possibly afford would be a stretch and a downgrade from our rental.”