A girl I went to high school with does this kind of thing constantly. She's always accusing people of doing these horrible things to her (she, too, claims she's been raped by mysterious strangers), even when there are witnesses who say, "Wait, I was there, that didn't happen." It's been going on for years; I remember, back in the day, she claimed a guy from our school physically attacked her and injured her really badly; this supposedly happened in public, with witnesses. Several of her friends were there when it supposedly happened and were like, "He never even touched her." So no one believes her stories, which is probably the case with your friend (or, the few people who DO believe her, will eventually figure it out).
It's sad, because she's clearly mentally ill but not getting the help she needs -- and while I want to feel bad for her, it's extremely shitty that she falsely accuses people of things. She also does stuff like going on FB and ranting about how guys she dated 10 years ago supposedly did her wrong (like, she'll call them out by name and make up these incredible stories about imagined wrongs -- some of these are guys she maybe went out with once or twice or barely knew). It creeps me out but I can't bring myself to delete her and miss out on the drama.
Recently, her aunt sent her a long email calling her out on all the lies. She then posted the email, in its entirety, on Facebook, looking for sympathy. Like, "Can you believe how vicious my aunt is to me? How could she say these things?" But I knew everything the aunt wrote was true. Not a single person commented on it or acknowledged it (not one "oh, you poor thing," which is what she was going for, I'm sure). The aunt actually sounded like she was trying to help her. It's really bizarre and sad.
That said, I'm living vicariously through you for calling your friend out. There have been SO many times when I've wanted to reply to this girl and be like, "That absolutely did not happen. You need help."
As an aside, I normally want to err on the side of believing a woman who says she's been assaulted, but when someone is CLEARLY lying, it makes me furious. Stuff like that goes unreported far too often and for someone to lie about it is reprehensible.