I'm just going to type out the full story rather than being vague.
We have a girl named Oceanborn, a black cat who never grew up - she has looked like an eight-month-old kitten for years.
When we got Oceanborn, she was five or six months old. She was a little shy but we could play with her and pick her up okay. Shortly after getting her, she got a very nasty eye infection that required a course of antibiotic drops. It became clear pretty quickly that she *really* did not like the drops, and giving them to her became a task for two people. We felt that it would be a bad idea to stop the antibiotics early, so we finished the course.
It was clearly traumatic for her, and I still feel awful about it today. She became terrified of us. At that point I felt it would be best to give her space. I was really hoping that time would heal that wound, but it's been about four years now and there's only been tiny bits of progress. She will let us pet her, but on her own terms - if I approach her she will likely run. I haven't had much luck with using foods to get her to warm up to me. She is okay being out and about when we are home, but if there is a visitor she will hide for hours.
She lives with another cat friend who is very social and full of energy, but she only interacts with him occasionally.
I'm honestly not even sure if I should be trying to get her to open up or not, but it really eats at me so I'm reaching out for suggestions. I want her to be the cat she could have been without the trauma, but maybe that's being selfish and she is who she is? I think I need an outside perspective because it's too emotional for me.