One thing I know is that you constantly lose things and get gear stolen. Hammocks are worthless for long term and sleeping bags are also no good. If you have gear you can't keep on you at all times than expect you will one day lose it.
Homeless in an urban environment really ask for multiple pairs of socks. Lightweight and worth their weight in gold to ensure you can keep on your feet without them rotting off. Chewing on sticks are your best friend for dental hygiene.
Clothes, clothes and spare clothes is what matters. Keep your equipment simple and plain so its not desirable for theft