Is there any type of hospital that would allow for an extended stay, but the patients would be able to check themselves out if they so wanted? The check-out process does not need to be easy. What would the terminology surrounding it be? Would some sort of rehabilitation center provide this?
This is modern day and in the United States, and would be dealing with mental illnesses that aren't considered as dangerous, like anxiety disorders, bipolar, and eating disorders.
If there is nothing that fits those parameters, are there any sort of rehab clinics that allow for extended stays, and deal specifically with eating disorders and cutting, not drugs?