Handling suicide threats is really anxiety provoking, so I feel for you. I've had to deal with this a lot with my exBPDbf and the very first time I panicked. Try to remain calm and be supportive. It's impossible to know when a threat is 'real' or not, and the fact is that we should treat all talk of suicide as a real risk. You must remember that you yourself are not an expert or trained professional and that what is important is that if she is having these feelings, it is the help of such individuals that she needs.
Does she undergo any treatment presently? If she already has mental health team involvement, then she may have a crisis management plan. If not, I'd advise you to encourage her to contact a crisis support line. There is even a text line that can be used if she doesn't feel like engaging verbally with someone. She can text Hello to 741741 and open up a dialogue with someone who is accustomed to supporting people in crisis.
Here's the link to our Safety First document on the site, which has a section for Suicidal Ideation and may help you to be prepared for what to do when these situations come up. I hope it is helpful.
Safety First.
Take good care of yourself. Having someone in your life who is prone to crisis is extremely stressful, so be mindful of your own limits. Getting drawn into a drama with a person who is feeling unsafe is not good for either of you. Try to focus on the end game of getting her to engage with the help that she needs, without being pushy. There is good advice within the link, so take a little time to brief yourself on it if you are taken unawares and you have the opportunity to prepare yourself before responding. Knowing what to do and say in such an emotionally triggering situation can take a weight off you.
Love and light x