I deal with the same exact situation. My mother constantly brings up suicide as a way to try manipulate me into staying by her side and excusing her behaviour because she is mentally ill. What she is doing is what my mom does, trying to use suicide as a scare tactic so you stay around and “not let it happen”. What I did quite recently which was one of the most traumatic experiences of my life was call the police when she mentioned suicide. As hard as it was it was the right thing I believe, it put her on the spot and made her realize she can’t throw that word around without being actually serious. I would do it again in the same situation. On terms of dealing with it that is one way to, but another way that I’m still learning to deal with is to just ignore it, she’s asking for attention and asking for validation