Homelessness was the condition of not having a home to live in.
After being stranded in the 20th century, by 1996 captain Braxton was living homeless on the streets of Los Angeles, his only belongings being the contents of a single pushcart. (VOY: "Future's End", "Future's End, Part II ")
In 2373, Starfleet Captain Benjamin Sisko ordered the USS Defiant to fire two quantum torpedoes with a trilithium resin payload into the atmosphere of Solosos III, despite warnings by Michael Eddington that those actions would leave hundreds of thousands of people homeless refugees. (DS9: "For the Uniform")