The short answer is “no.” The course of BPD is very different from person to person. While there is evidence that there is actually a very good prognosis for many people with BPD, some people continue to have symptoms of BPD over time and even after treatment. There is no way to foresee the outcome for any particular individual, probably because there are many factors that go into predicting recovery (e.g., motivation to change, genetic/biological BPD causes, resources).
However, there is research to suggest some general factors that predict better or worse prognosis. For example, there is research to suggest that people who have BPD and a history of childhood sexual abuse have a harder time recovering from BPD. In addition, people with BPD and co-occurring substance abuse or antisocial personality disorder are less likely to recover from BPD. This is not to say that people with these factors cannot recover from BPD, but it suggests that these factors make recovery more difficult.
Paris J. “The Treatment Of Borderline Personality Disorder In Light of the Research on Its Long Term Outcome.” The Canadian Journal of Psychiatry, 38:28-34, 1993.
Skodol AE, Siever LJ, Livesley WJ, Gunderson JG, Pfohl B, & Widiger TA. “The Borderline Diagnosis II: Biology, Genetics, and Clinical Course.” Biological Psychiatry, 51:951-963, 2002.
Stone MH. “Long-Term Outcome in Personality Disorders.” British Journal of Psychiatry. 162:299-313, 1993.