Re Australia, it's run by the states. I'm form South Australia, which has 'Housing SA'[1], currently live in Tasmania where the service is called 'Housing Tasmania'[2] These services will help pay / pay in full a bond for private rental, as well as co-ordinate the renting of government owned housing. Houses, town houses, units, and flats, in a variety of locations throughout a city.
If you're a welfare recipient the typically arrangement is for the rent to cost somewhere in the vicinity of 1/3 of your payment. Full rate Unemployment benefit in Australia is $600 a fortnight including something like $100 a fortnight 'Rent Assistance' payment. I believe welfare payment for people unfit for work for whatever reason is slightly more.
Australia also has fairly good services to homeless and disabled provided by the outreach sections of church organisations. Salvation Army and Mission Australia are the two I'm most familiar with. These services will, in certain circumstances, furnish a home and supply clothes.
We still have homelessness. Services are still stretched to their limits. There's a waiting period for the able-bodied to get in to public housing. We still have rough neighbour hoods.
1. https://dcsi.sa.gov.au/services/housing-sa
2. https://www.dhhs.tas.gov.au/housing