I work with people who WERE on the street or now one step away. People with mental problems that employers will not hire. With disfigurements that make them "not fit for public consumption". And I see 70+ older adults who worked their asses off all their lives, but who got a serious illness or had a spouse die of an illness, and now are living on $900 a month for rent, a car, utilities, ($250 a month),  & medical...who live each day watching TV - the only entertainment they can afford. 
No, only a percentage of the homeless/criminals are certifiable. Given my background in psychology and talking and watching them, I'd say the rate is 3x that of the national average of 18%, or roughly half. Another 25% are just milking the system. And the rest have addictions or disabilities/disfigurements. 
Yes, some will scam the system for food & shelter so they can have money for drink  & drugs. And some rich scam the system to get a 3rd home, a yacht, and vacation in Europe. What's worse?