This is already happening. Compelled vaccination is completely different than a mentally disturbed member of our society roaming the streets unhinged. I have been party to several title 36[1] cases and it's very, very difficult to get dangerous people "petitioned". It requires coordination between disparate agencies like hospitals, Fire/EMS, Police, community mental health orgs, etc. None of them share a database.
Once they are found to be incapable of living on their own, what do we do with them? Jail? Hospital? Half-way house/Assisted Living?
I will tell you... They end up back on the streets and it isn't pretty. The underbelly of every American city is a nasty, grimy, horrific place. I need to retire.