Do people with fearful-avoidant personality come back?

My ex gf broke up with me about 2 months ago and she hasn't really been in contact other than to say good luck on my summer class. Since then she has blocked me on Snapchat and Instagram. She told me after breaking up via text and playing the blame game, that she needed to cut me out of her life in order for her perception of me to change. Her and I have to work together in university coming up in September and I am still anxious about it all.

I have been doing some reading up on situations like this, and have been getting tips to look up attachment styles in adults. I found that she fits the fearful-avoidant category and it has got me thinking about certain aspects of the breakup. She did have a rocky past (previous ex bf abusing her etc.) and I feel like it had a bit to do with it all. There were times where she would act quite differently to me, she could be in a different mood in a matter of minutes. I do admit that sometimes I would have rough days and be in a bad mood overall, and she would usually pick up on that.

The breakup was very sudden as she seemed to be interacting with me as normal the days leading up to it. I'm not sure if there was really any warning signs, although the last time I saw her, she didn't seem quite herself. She said she had a couple nightmares with me in them where something would happen and I would break up with her or I would spread rumors about her...of course none of that is true.

I miss her dearly and I want to know if there is any possibility of someone with this type of attachment personality coming back to their exes. I also have to work with her at university and I want to show her that this person I've been made out to be, is not the person that I am. I want her to see the guy that she fell head over heels for (her words). Any thoughts on how to approach this? It will also make our group work dynamic a lot less awkward and easier to handle if her and I could try to see where things are at.