Many of the people I have met are other students who have come to Florence to learn to speak Italian. Many are people who work here who have come from other countries where jobs are not as easy to come by and some are like me, looking for another place to live that feels more like home in their hearts. . Many of these people do not have work visas and are here illegally, selling merchandise on the street, also illegally.
Even though the news in the US only has information about the USA immigration problem, it is in no way isolated there. Other countries have borders also, and other people want to go into them! It doesn’t seem that Italy has a good solution either. It is interesting to note that they have signs warning tourists not to buy from these "black market" vendors. The signs are in Italian, so if you don’t speak the language, you will probably miss it. Guidebooks usually indicate this to be so, but the difficulty is in determining who are "black market" vendors.
Some of the vendors carry fake designer purses around in white sheets which they must set up and pick up 50 times a day, or whenever the police come by. Interestingly though, they only wrap the merchandise in the sheet, and stand there until the police go by and then set up again. There are vendors who sell purses, sunglasses, toys, scarves, and when it rains (rarely) umbrellas.
These vendors are on all of the piazzas. I have never seen the police say anything to any of them, but once I saw an officer yelling at a lady who purchased a toy from one of the vendors for her child who was standing nearby. It is definitely buyer beware!