There is so many homeless cats that need our help! You could help them by only resteeming stories like yours.
Somehow your story reminds me mine.
About five years ago, when we moved to our house and after we finished major renovation, there was this very bone skinny homeless black cat, she was hiding behind the small tree next to our garage and you could tell she was so hungry, we immediately thought that her previous owner must have abused her or something bad has happened to her in her past.We started calling her Sisi. Sisi was so scared. When we opened our storm door she immediately run away. We put some food next to the tree where she usually came and hoped she would come back. A few minutes passed, she came and ate all of it like she never ate before. After while she got used to us and started coming up the stairs of our back entry.

We fed her every single day, sometimes twice, in the morning and in the evening as well. Whenever she came we knew she wanted to eat or spend some time on our backyard. She loved to spend her time during the day in the sun.There was a period for about a month when she didn’t show up and we thought that she was probably gone. Then she came, she was so skinny, but we were happy that she was back. After a week Sisi gained back and since then she was coming to our backyard every day. You could tell she was happy outside as long as she had something to eat. On December 28th 2017 I went to our basement and my wife was talking to someone, I said “what is going on?” she said “we have a visitor” and there she was “Sisi” in our basement. I always knew my wife would try to do something to help Sisi even more, because she is the biggest animal lower I have ever known. Outside was so cold (in NY felt like -8F) my wife got her somehow inside our house. You could tell she was sick. We discussed what to do with Sisi and we decided that after the extreme cold is over we would let her go and keep feeding her every time she comes. She was so scared. When my wife tried to pet her she was shaking and also urinated. She also had both eyes inflammation and difficulties with breathing.The next day She was still scared cat, but she let my wife wash her eyes with the black tea, we heard this would help and since we don't have any eye drops or antibiotics we tried the natural way. After two days she let us pet her and I could tell that she is not afraid anymore. On the new year’s day Sisi ate all her food and you could tell she felt much safer, even though she was still spending most of her time in her little space she chose for-herself. The next day we went to vet without Sisi. We explained him our story, told him that it would be impossible to bring her in, so he gave us antibiotics for her. After two weeks of giving her antibiotics mixed with food she was a healthy cat. No difficulties with briefing and eye inflammation was gone as well. But you could tell she missed her freedom, so we decided to let her go. To this date she comes to our backyard every day and we are happy we could help her. Even though she is a wild cat, we still love her and fell like she is our cat.
I just noticed while writing this it takes so much space in your comment section, so for that I apologize.