Government more than any other organization, enterprise, or institution can completely eliminate hunger, homelessness, and all poverty in general. The people you mentioned don't want to get a full-time job, because they'll lose their guaranteed government income. If you get a job, working for one of the many privately owned business enterprises/dictatorships/fiefdoms, the bosses can fire you for whatever reason and you end up without an income hence people choose to remain unemployed. I believe the government should provide guaranteed employment rather than a monthly check. However, if you're going to give people a monthly check then don't take it away when they get a job and start working. I have a friend who was on a non-service connected disability pension from the VA for several years, and he told me that he would get a job and start working, if he could continue receiving his VA disability, for one or two years, while he works, saves money, goes to night school to learn a trade, etc. But they prohibited him from working, so he moved to a third-world country, where his VA check allows him to live well.
The big money capitalists and even Milton Friedman, one of the icons of free-market Libertarianism, promoted the idea of giving people a monthly income: