If this woman has MH issues and refuses to get help that is a great shame but, like everyone else, she is not entitled to make someone else's life hell & she is responsible for her own health. Since diagnosis & treatment can only be made by a health professional, that's why it's important to call paramedics or her local GP if she is believed to be at risk. It's important to say that, if she successfully killed herself, it would not be your brother's fault.
That said, I suggest you and your brother need to do some reading around the subject of coercive control and emotional abuse. Both are soon to be outlawed on the statute books. Isolating victims, manipulation, lying and abuse are very common traits in coercively controlling people and it doesn't necessarily follow that they are mentally ill. It's precisely by setting up an image of being a sparrow with a broken wing that some lure in a victim in the first place. "You are the only one that can save me" ... "I had a bad childhood".... "We don't need other people, just our love" is the appealing type of stall they set out. To maintain control they alternate glimpses of loving, kind behaviour with frightening, intimidating, irrational behaviour.... like threatening self-harm and so forth. The ultimate effect is to create a co-dependency whilst at the same time crushing the victim's spirit. The same techniques are used by professional torturers, in fact.
Your brother has done extremely well to get away if he's experienced the latter. Coercive control is a horrible thing that destroys victims' self-esteem and makes them question their own judgement. The effects last long after the relationship finishes. The guilt and fear sticks around, as does the fantasy of the nice kind person they were first attracted to.
There is an online resource called the Freedom Programme which is principally aimed at female victims of this behaviour but which your brother may find useful in the transition.