Is it common for persons with BPD to go as far as to commit a crime and blame others?
Does not surprise me at all. I saw a BPD write a check for hundreds of dollars for a service she received, and then cancel the check right away, giving me some ridiculous excuse about how the service wasn't up to par.
This same pwBPD would tell me things like, "It's a dog-eat-dog world, you gotta be careful out there." I think she thought that everyone is out to get everyone, so you better one up others first. Of course this is not how the world really works -- most successful people achieve success by cultivating long-term, mutually beneficial, trusting relationships with others.