Here are the top 4 google results for "Can BPD be cured?":

bridgestorecovery.com/borderline-personality-disorder/can-bpd-be-cured/#:~:text=Borderline%20personality%20disorder%20(BPD)%20cannot,in%20intensity%2C%20or%20entirely%20eliminated.

Borderline personality disorder (BPD) cannot be cured, and anyone who enters treatment looking for a quick and easy fix is bound to be disappointed. However, with treatment the symptoms of BPD can be effectively managed, monitored, and ultimately reduced in intensity, or entirely eliminated.

https://www.verywellmind.com/is-there-a-cure-for-borderline-personality-disorder-425468

While there is no definitive cure for BPD, it is absolutely treatable.1 Lenzenweger MF, Lane MC, Loranger AW, Kessler RC. DSM-IV personality disorders in the National Comorbidity Survey Replication. Biol Psychiatry. 2007;62(6):553-564. doi:10.1016/j.biopsych.2006.09.019 In fact, with the right treatment approach, you can be well on the road to recovery and remission.

While remission and recovery are not necessarily a "cure," both constitute the successful treatment of BPD.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4500179/

Research during the past 2 decades has clearly demonstrated that BPD has a positive trajectory over time. Although it is a disorder associated with many psychiatric and medical comorbidities, many of the most troubling symptoms remit during the first few years. Unfortunately, several of the underlying personality traits remain for longer periods, and these are the elements of the disorder that may not be fully addressed by current treatments.

https://embarkbh.com/blog/borderline-personality-disorder/ask-a-therapist-can-bpd-be-cured/

While BPD can’t be cured and won’t go away, Gatlin said the prognosis can be good for those who are going to therapy and taking medication, if needed, to manage their symptoms. She noted that a key milestone is when a young adult reaches their mid to late 20s, as that’s when the brain finishes developing. Once that process is complete, your son or daughter can better navigate their mental health.

Look at it this way: Imagine your leg was amputated and you had to get a prosthetic. With time, and physical therapy, and a leg that matches your needs, you'll eventually be able to walk, run, and jump again. But you'll always rely on the prosthetic leg, and there are some things you'll never be able to do. You might have a leg that's better for soccer and a leg that's better for sprinting, and you'll need to switch legs to keep up with two-legged athletes. And you might end up surpassing two-legged athletes at some things. It's still a disability, you're still disabled, but it's effectively treated. My NPD and your BPD are like that missing leg. We have tools to solve our problems, and we can get really good at using them, but the fact we still need them means we're still disabled. And at the end of the day, no amount of skill is going to help us if a fully abled person decides that today they hate "cripples", or they hate "borderlines", or they hate "narcs".