Without an awareness they are ill people have no rationale to take medication. Psychotic people are hospitalized because they are a danger to themselves and the general public. Usually the offence is a minor one but people in a psychotic episode can be unpredictably dangerous, especially if they have a concurrent substance abuse problem, and they need prompt medical attention. The person is not violent or evil in any sense of the word. The psychotic episode is driving the individual to behaviour that is out of character for them.
Some people avoid homelessness through their families support.
Living in their parents basement for example, they are never treated because they never reach a threshold of dangerousness, but they would be unable to care for themselves without their family's financial support. The people most at risk for violence by someone in a psychotic episode are the immediate family members. That places tremendous stress on family relationships and people with schizophrenia tend to lose human relationships over the course of their illness. About one third of the homeless in North America are suffering from schizophrenia and have no awareness they are ill. They are people who have lost human relationships to the symptoms of schizophrenia.