Federal agencies each have their own definition of “homeless.” Health centers funded by the U.S. Department of Health and Human Services (HHS) define it a little more broadly than the U.S. Department of Housing and Urban Development (HUD).
The agencies use these definitions in determining who is eligible for services, in addition to their other eligibility requirements. Details here.
“According to a 2002 national study by the Urban Institute, about 45 percent of homeless adults had worked in the past 30 days — only 14 percentage points lower than the employment rate for the general population last month. The number of working homeless would probably be even higher if “off the books” work was included.” — from “Five Myths About America’s Homeless” by Dennis Culhane in the July 11, 2010 New York Times.