You prove you're homeless by being willing to take showers in a public facility. It's easier than voting.
There was this bishop,see,who got to talking with a guy out in St.Peter's square, and he discovered that it was the man's birthday,and the bishop invited the man in to have lunch with him and the pope. The guy turned him down, because he said he hadn't had a shower in so long that he would feel awkward about hanging out with the pope. The pope heard about it, and felt bad that someone would feel that their personal cleanliness kept them from talking to him, so he has ordered public showers to be installed. (They already have public toilets.)