Hi, 4/10/62, and welcome!
It is understandable that you want to help your MIL. I can tell you care about your husband and want to help him, too. BPD is a disorder that causes a lot of pain for the person who has it and their entire family.
Turkish has shared some good resources with you. Suicide threats should always be treated with seriousness; at the same time, it is also important to have boundaries so that you will not be manipulated and held hostage by those behaviors. Have you or your husband ever sought professional guidance for yourselves? A good therapist can be very helpful in navigating this kind of relationship.
One thing to keep in mind is that you cannot make your MIL see that she needs help. There may be a situation in which emergency professionals may involuntarily admit her for psychological help (i.e., in a suicidal situation), but even then she is unlikely to seek continued treatment. The person you can help right now is you. You are here, and that is a good step.
Getting Our Values and Boundaries in Order is a resource that helped me when I first came here. Learning to identify your boundaries and honor them will be very important. One tool that I have found very helpful for communicating my boundaries is
TOOLS: S.E.T. - Support, Empathy and Truth.
I hope you will keep looking around and let us know how things are going.
Wishing you peace,
PF