Synonyms of 'homeless'
destituteDictionary, exiled, displaced
the growing number of homeless families
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a newsreel of abandoned children suffering from cold and hunger
all kinds of displaced and dispossessed people
If you describe someone as down-and-out, you mean that they have no job and nowhere to live, and they have no real hope of improving their situation.
He looked unshaven, shabby and down-and-out.
Thesaurus for homeless from the Collins English Thesaurus
Homeless people have nowhere to live.