The mental illness portrayed in "Possessed" is what the Victorians called hysteria. It consists of being a woman and being treated very badly by a socially and sexually superior man.
David Sutton (Van Heflin) is an unthinking cad who wanted casual sex with a vulnerable, lonely employee from a nearby holiday house. Being his social inferior, Louise (Joan Crawford) thought she could improve herself by going all the way with him (a big deal back then because birth control was so primitive). This rash move causes her to get desperate when she senses David's coolness, and then deeply wounded and enraged when he callously ends their affair.
Although the movie attributes it all to "love", it is her sexual betrayal by David, and the casual arrogance of his superior social status, that unbalance her. Moreover, things go wrong at her residence, where she works as a servant or nurse to a married woman who falsely accuses her of involvement with her husband, an accusation that is echoed by the returning daughter. This further injustice by her social superiors drives her unhinged.
The story is told in flashback after she goes into a "hysterical" trance on the streets of downtown Los Angeles. There's a lot of psychiatric lingo around her treatment and confession, but the illness is no "hysteria", it is frustrated outrage against social and gender injustice --- only Hollywood can never tell it that way.
Above all, women could not be told the truth about their condition after World War Two, when they had to be driven out of the factories where they had worked beside men and back into the home to be consumer housewives.
This is really a Victorian throw-back morality tale: it was exactly the kind of case with which the Sigmund Freuds made their name by locking up troubled wives and daughters in Imperial Austria. That said, it's a well-told yarn with great studio sets and a strong central performance. Note the cameo scene at the bar between Geraldine Brooks and Van Heflin. When he takes his eyes off her to ogle the cigarette girl, Geraldine says: "That's so American, wanting more than you've got!" Yes, this film fails to get to grips with the underlying issues, but it's enjoyable "noir" fiction nonetheless.