You cannot talk about the homeless as some monolithic group of people that are all the same. Some of them are schizophrenic and their nature is crime because their brain is haywire. Some of them are addicts (both legal and illegal) who would be nice people if given treatment for their problem. Some are at nice people, but they are at the bottom of the intelligence chart (not to be confused with IQ, but instead what people think of as intelligence despite it not being well defined) and mentally unable to hold a job that could support themselves. There is a lot more, but I'm not a homeless expert. The above are just specific people I know (either family or family of close friends).

Some homeless are also criminals, some are not. Some of the criminals would turn away from crime if given the proper help, some will not. Some of them will refuse help unless it is forced on them - we have as a society rejected the needed force because of rampant abuse in the past. Each situation is different. Some of them are easy to solve - most are not.