When Steven McDonald moved to the United States from Jamaica, he and his brother dreamed of owning a home. For two decades they saved and hoped until, in 2011, they were able to buy a two-family house in Springfield Gardens, Queens.

It was a perfect fit: walking distance from the LIRR and close to a park where McDonald’s son could play. “The minute we pulled up to check it out, we knew, yeah—if this is within our budget, this is it,” McDonald said.

But a few years later, after the mortgage became …