One, you choose your occupation.
Two, if you really want to reduce redundancy just use "person/people." Everyone knows if you say "homeless person", that that person is, in fact, a person. Seems like an extra word there.
If you want to be precise and point out someone is homeless, use "person, who is homeless." If two words and a comma is too redundant for you, see my first point.
Reduce redundancy. Other "occupations" do this as well. You say "painter", not "people/person who paint(s)".