I have dealt with this for the last 9 years.
My step-sister, who I have known since I was 2 & she was born (long story) and I reconnected after my son was born and my mother & her father became a couple.
It began simply as us having shared interests, as I do with my friends, and really enjoying our time together.
It escalated to her mimicking my behaviors, attitudes, clothes, everything down to what soap I used. My ex-husband called her my girlfriend, and accused her of having a romantic obsession with me. I think that is not the correct diagnosis, but speaks to the extremity of the situation.
She wanted to spend all our time together, and would become hostile if I did things with other people, even if I invited her & she just couldn't come.
I tried on numerous occasions to have a healthy dialogue about boundaries with her to save the friendship. I gave her a lot of passes because she was "going through hard times" or "had a few too many beers", whatever excuse I could find.
My concerns were met with rage, verbal abuse, crying and threats of physical violence that have on a few occasions become more than threats. The next day, she acts as if nothing has happened. If I try to talk about it she gets very rude and says I "shouldn't go there if I know what was good" for me. Eventually I just began to put distance between us. This only served to anger her more, and she would lash out at me unprovoked in many situations, both publicly, privately, and via text and email. Only to contact me days later, as if all was well, wanting to get together and do things we have always done as friends.
Because we are related now and also have many of the same friends (we grew up together after all) it has been impossible for me to separate myself from her completely. I try now to avoid being alone with her, to avoid saying anything that can set her off. Basically, I walk on eggshells. While we can still have decent times which make me miss my good friend, it often becomes very bizarre, there is often the yelling and she has gotten physical on occasion. I go to group events with a lot of anxiety. She blames me for the corrosion of our friendship & to a point is correct to do so. I do avoid her as best I can.
She has run her mouth about how awful I am to many people. Anyone who believes her opinions of me does not know me & I can't be bothered by it. They all learn eventually and come to apologize and warn me about stuff she is saying. I do not engage them, I don't need to know. She is a sad case, and that is all there is to it. I can't tell others how she is because it is something one must see to believe and I am not going to add to her troubles by announcing her issues to our mutual friends.
People who have normal friends and healthy friendships can't understand how destructive these kinds of people can be. Even I didn't get it and let things drag on for a lot longer than I should because, on the surface of it, of course your friends should share your interests and be able to participate in your life, right? She has shown me a lot about boundaries and my tendency to placate people and avoid conflict. I tend to be "nice" to people, which is not always the same as being good to them. It is something she has helped me recognize and work on, and my relationships are healthier for it. Unfortunately, until she gets help, we will never have a healthy relationship. She is, at this time, incapable of doing so.
I am honestly unsure there is help to be had, and looking back through our lives see she was always this way, except now she is better at it.
Good luck to you. You have to keep telling yourself that you did the right thing by ending the friendship and not get sucked into feeling like you abandoned her.