Earlier quoted context omitted.
No, the alternative is to have the government build subsidized housing and then enact strict price controls so that even poor families can afford to live reasonably. That's how it was done in Singapore for example and is why they can live in "spacious" 30-70 m^2 apartments despite having a higher population density than Hong Kong. See also http://en.wikipedia.org/wiki/Public_housing_in_Singapore .
I disagree it is the governments job to give people a place to live. From the sounds of it, Hong Kong already does a lot of this. At some point, people need to take care of themselves.
Moreover, a hungry homeless person is a security risk. How many iPhones, GPS's, laptops, etc. are stolen in a smash-and-grab incidents? How many people get hurt? No, not by your friendly neighborhood homeless lady, but by a person who feels they have no other choice but to steal or a person who is hooked on an addictive substance and can't stop?
Poverty also does not take a lot of people. A few percent here and there will cause enough headaches to become noticeable.
And poverty is chronic in society. It's not like if you took all the homeless, poor, and hungry and shipped them off to some unknown land you'd rid of the problem. No, instead more people would be pushed into the margins, becoming poor. You have to treat the cause.
Therefore, if poverty is inherent in certain societal setups, if it is everyone's problem (i.e.: everyone pays the cost) and it takes only a small percentage of people being poor to become a big problem, it is in the interest of everyone to change the societal setup so that poverty is minimized. Your original point was that it's not the government's job to do this. I argue that it is. The government (by the people and for the people) would not be doing it's job if it wasn't taking care of me or the person next to me.
As an aside, some might argue that private charities work much more efficiently than governments when it comes to homelessness/poverty/hunger. Personally, I believe a balanced approach works best. Big slow moving government projects with lots of oversight and restrictions coupled with flexible and quick-acting private charities are much more effective than either of the two.