Hi Forestgirl,
Welcome aboard.
Coping with BPD traits and behaviors can really be frustrating. Unfortunately, something as innocuous as an A/C unit shutting off can trigger major dysregulation. Learning about the behavior and understanding is essential for being in a relationship with a person with BPD (pwBPD). I think it is great that you are being supportive by wanting to know more about the behavior of pwBPD. Being supportive and understanding truly makes a difference in a relationship with a pwBPD. Here is a beginners article that describes the basics of a relationship with a pwBPD.
The Do's and Don'ts for a BP relationshipThe emotional turmoil inside a pwBPD is absolutely horrible. Most pwBPD grew up in an invalidating environment, where their caretaker did not validate the pwBPD's emotions or gave negative reinforcement of averse emotional expression. Essentially, the pwBPD was taught, learned, or was invalidated by emotional responses. The core of the disorder is emotion dysregulation (learning to control emotions).
The comment your SO is making about having no purpose in life is related to having an unstable sense of self. Many times a pwBPD will have a self-image reliant on the premise that they are "bad" or many times they feel as if they do not exist at all. The lack of a stable sense of self can be exacerbated in situations when a pwBPD feels that something is lacking, such as support or nurturing. Although this may not be the case, since pwBPD view feelings as facts.
It is good that your SO is somewhat self aware. Is your SO in therapy?
Learning about the disorder and wanting to help is great, but as partners of a pwBPD there is a tendency to forget about our needs. Don't forget you are important too.

Take some time to read the lessons on the right hand side of the page. They really do help. Also, posting here really helps. There are so many people going through similar situations.
Perhaps you can share more of your story so we can help you better?