There were times, a decade ago, when the Road Home, the largest homeless shelter in Salt Lake City, was so full that families trying to bring their children in from the streets for the night would be turned away. “Heartbreaking,” is how Matt Minkevitch, the Road Home’s executive director, remembers it. He had spent nearly three decades helping the less fortunate, and was on the hunt for fresh solutions to the intractable problems he saw. Minkevitch figured he could accommodate the overflow if he could find another place for his longest-term residents – the “chronic homeless.” Although they accounted for just 15 percent of the city’s homeless population, they consumed a disproportionate share of the shelter’s resources. But they were also the hardest to house.