Usually yes, but it depends on the context.
While not being within an intimate relationship, they won't have anyone to strongly trigger their wounds and no one to whom direct their emotions and create conflict with, which then may result in greater stability. On the other hand, the lack of having someone to care for them may make them struggle with loneliness and feelings of unworthiness.
I believe that for someone who is deeply affected, the most stable setup is to live by themselves while still having people who can provide support on demand at a close reach, given that those supporters will never get personal, even if attacked. That may be unrealistic, but there is one setup that is close enough to this. It is a psychiatric hospital that has a private room for the patient. Not a life-time recommendation, but might be the best route when things really go awry. And the controlled/balanced hospital food may also be beneficial, IMHO.
There is a renown psychiatrist in Brazil named Ana Beatriz who explicitly asks her BPD patients to remain single for the length of their recovery, so that together they (patient and therapist) can find out her real identity, preferences and desires. I believe that being stable is also one of the reasons why she asks for this. Here is one of her videos on BPD topic:
https://youtu.be/Wrmb5zteFAI
