If you want to make sure there are no homeless people then you simply give everyone a home. Shelters don't count because they are designed for homeless people. If you are in a shelter you are homeless, if you are not homeless you aren't in a shelter.
How would 'simply give everyone a home' work? California is the most expensive real estate in America. The state is spending 13 billion a year on triaging itinerants, many of whom refuse sobriety rules that may put them on the path to free housing.
There is a giant homeless industrial complex siphoning out money intended for the homeless on management, top price union labor to modify motels bought with tax payer funds at way over valuation price that will 'house' a few dozen people in former hotel rooms.
What would you do to house anyone who wants a home?