Naomi’s Way, a 12-unit shelter in New Brunswick, N.J., had been providing transitional housing for special-needs single homeless women and their children.

About a year ago, Catholic Charities, Diocese of Metuchen, N.J., which operates Naomi’s Way, decided to convert the building to permanent housing. But it only had about $100,000 for much-needed renovations, and its initial plan was limited to redoing the kitchens in each apartment and making other, cosmetic changes, like replacing sliding closet doors with doors that swung open.