80% of homeless are homeless by choice and they don't want help or housing, etc. You can't solve that "problem". It is what it is. Help yourself.
Discussion
We need a few words for different tyoe of homelessness. You're right, some choose it. It is a lifestyle for some even. Others suffer through it. We need more words..
Lifestyle homeless
Drug addict homeless
Mentally ill homeless
On side note I remember renting and feeling a sense of "homeless". Again this is why many definitions are needed. While renting I felt I truly didnt "have" my "own" home. While living with parents that home always felt like mine too. Not until I owned a home did it feel "mine". Renting, I never felt the landlord was actually sharing the home with me to be "mine".
Again this is why the term homeless needs many definitions.