How does SSA define homelessness for the Living Arrangement question?

Homeless/Transient (Living Arrangement): A transient is an individual with no permanent living arrangement, i.e., no fixed place of residence. A transient is neither a member of a household nor a resident of an institution. 

Examples:

• a homeless individual (i.e., someone who sleeps in doorways, overnight shelters, parks, bus stations, etc.); or
• a person who stays with a succession of friends or relatives and has no permanent living arrangement on the first moment of the month.

(Source: https://secure.ssa.gov/apps10/poms.nsf/lnx/0500835060)