I did this for awhile after I got my PC game. I made my guy look like the typical California hippie. San Francisco is full of street performers of all kinds, many of whom are homeless. I gave my guy a guitar and the virtuous trait, so he could learn to play for tips quickly. I gave him the mooch trait so that in a bind, he could beg. I gave him the insane trait so that he could talk to himself and keep his social meter up and I think that provides a bit of fun as well. He can also rumage in the garbage with that trait. And I gave him a dog. Lot's of homeless people have dogs.
His dog is a mutt of husky breeding and he has what would be very typical traits for a husky, that of adventurous, independent and friendly. Husky type dogs would take well to the wandering lifestyle. They love roaming around with or without their humans.
My guy lived in a park by a pond for a long time, used the public restrooms, didn't bath very often. He played his guitar in town until he was discovered by a famous rock star.