Your concern is a very common one. Most people who receive the diagnosis of borderline personality disorder need some time to adjust to the news. Unfortunately, there is a lot of misinformation out there about BPD.
One very common myth is that BPD can not be treated. In the past, experts did believe that BPD did not respond to treatment. However, in the past two decades, a number of new treatments for BPD have been developed (for example, dialectical behavior therapy), which has been shown to be effective in reducing the symptoms of BPD. Medications have also been shown to be helpful.
So, does this mean there is a cure for BPD? Not exactly. There are a number of effective treatments for BPD. These treatments can result in such substantial symptom reduction for some individuals that by the end of treatment they might be considered "recovered" or "cured."
But, not everyone experiences such dramatic symptom reduction. Many people who undergo treatment for BPD continue to have some symptoms, but find the symptoms to be much more tolerable, and report that they are able to function far better in their lives. The bottom line? There are treatments for BPD that are remarkably effective and may produce a "cure" in some people. But, even for those who do not fully recover from BPD, treatment is extremely helpful.
Clarkin JF, Levy KN, Lenzenweger MF, Kernberg OF. "Evaluating Three Treatments for Borderline Personality Disorder: A Multiwave Study. American Journal of Psychiatry, 164:922-928, June 2007.
Feigenbaum J. "Dialectical Behaviour Therapy: An Increasing Evidence Base." Journal of Mental Health, 16:51-68, February 2007.