Why does this job need to be given only to homeless people? If they are paid less than a normal worker would be (and they are, since they aren't paid anything at all), I'd say this is profiteering off the poor.
I would imagine anyone can take it. It's just that homeless people just happen to be the ones that have the most free time and gain the most marginal value from money. And there is no such thing as a "normal worker"; each job has its own required set of skills and its own supply/demand curve so you can't really say one kind of work is more exploitative than another.
Take a moment to view this video. Perhaps you, the reader, will gain a different perspective on this important issue.