We adopted my cat back when we were living in Chile. We lived in a very poor area and every saturday a group of women would gather at the local square and give up puppies and kittens they had found on the streets for adoption. So one day we went there and found this white little kitten and decided to adopt her. She's now 12 years old, living in Sweden with us and just as grumpy as always!
I do have a story similar to yours, although not with a cat. When we lived in Chile a dog adopted us. She lived on our street and had seen that we had a dog in our back yard, and she also realised we were friendly as we would always pet her when we saw her. So, stubborn and determined as she is - one day she decided that's where she was going to live! So she started sneaking in through our fences and into our house, almost on a daily basis, jumping up in our couches and just showing us that this was her new home, whether we liked it or not. Of course we couldn't resist the cute little mutt, and that's how she ended up coming back to Sweden with us too! Puppy (her name) is now 12 years old and a really spoiled princess- only sleeps on pillows in beds and couches and loves cheese more than anything. She has also starred in a short film here in Sweden with two of our most famous actors! Now that's a pretty good job coming from an ex Chilean street dog no one wanted! And she did it all by herself