Are there people who fall through the cracks? Yes.
However, if you are willing to play by the rules, in the US, nobody has to be homeless or go hungry. The problem is, the process is long and it requires you to basically be warehoused like cordwood.
Most Homeless you run into are that way because they have committed crimes and to enter the system will get them arrested because they are underage and will be returned to homes they don't want to go back to because they are being exploited, or because they are mentally ill and refuse treatment.
The problem is usually worst in Democrat-run cities because they don't want to pay for social programs and the mentally ill wandering the streets is an excellent wedge issue.
I worked in group homes, Transisional Living Programs, and Mental Health programs. 9 times out of 10, people are homeless because they want to be. The other 10 out of 10 is usually because they just became homeless and don't know what to do.
Once you experience working retail/fast food near an area with homeless people you quickly lose remorse. The shit I have to deal with pulls me to the dark side ever so slightly. The reasonable ones are the ones I don't mind interacting with but most of them are junkies.
To get on a social program, you have to give up the drugs. Most homeless won't do that, so they remain homeless.