Suki chose to live with us. She turned up at the local school where we worked and one extremely rainy night she followed me home. I let her stay inside and the next day sent her off again. She had come in the front door but somehow she found our back door, difficult as we are mid-terrace and she took up residence in the garden.
We didn't feed her for a few days but she still stayed, sleeping in my laundry basket under the lean-to. The vet contacted the owner who had moved away but Suki hadn't been happy so she had been given to another family but she hadn't wanted to stay with them either. So we feel privileged that she chose to live with us.