What a load of hippy smelling bull excrement!
Regardless if this person is in a bad way, slipped through the net etc then why should the OP have to pick up the tab for this persons misfortunes?
We have a social benefits and housing system in place to help these people, might not be perfect but is better than most people in the world get.
This comes from someone who had been evicted at short notice and forced into the social housing system. before anyone says anything I was working and paid the rent on time every month, made no breaches of my tenancy agreement, but pointed out the ways in which my landlord was breaching their responsibilities so they felt it easier to kick me out and find someone else than fix the issues with the property.