It is sweet of you to help this poor girl.
Now I don't want to be a damper, but I encourage you to practice biosecurity and quarantine your new found friend. Since she just suddenly appeared, you have no way of knowing what her health and condition may be. She may just be lost or someone may have let her loose because of illness or old age. It would be heartbreaking for you if she did have something that could infect your flock and cause everyone to become ill. Of course, continue to take good care of her like you are doing, check to see if she belongs to anyone, quarantine her to make sure there is no illness, then if all goes well slowly integrate her into your flock. I would search here on BYC to get ideas on how to do this. Here is one to get you started.
https://www.backyardchickens.com/t/12751/urgent-reminder-please-quarantine-newly-acquired-birds
Now I don't want to be a damper, but I encourage you to practice biosecurity and quarantine your new found friend. Since she just suddenly appeared, you have no way of knowing what her health and condition may be. She may just be lost or someone may have let her loose because of illness or old age. It would be heartbreaking for you if she did have something that could infect your flock and cause everyone to become ill. Of course, continue to take good care of her like you are doing, check to see if she belongs to anyone, quarantine her to make sure there is no illness, then if all goes well slowly integrate her into your flock. I would search here on BYC to get ideas on how to do this. Here is one to get you started.
https://www.backyardchickens.com/t/12751/urgent-reminder-please-quarantine-newly-acquired-birds