It took me sometime till I understood that was better to do not start taking care of homeless cats or dogs or other pets. I stopped when I saw the third one dying and again, not because of my fault. (the third one that died was a rabbit, before... a cat and a dog) I know that is painful to get attached and then to have to part away.

Here, in Canada, there are rarely homeless pets and you can find a good place for them if you can't take care of them anymore. Even for wounded birds.