"My" Stray cat is acting very, very strangely. She is slobbering at the mouth to were it is almost a puddle?

She is not really my cat because she doesn't live inside with me, she just stays out on my porch and I feed her. This has been going on for about a year now. I can't bring her in or anything because I don't really want to because she might be very dirty and she is also feral and runs at any sudden/fast movements I make. She won't let me pick her up either. Anyways, I just went out and I found her there, sitting at the foot of my porch, drooling. Literally slobber was hanging out her mouth and it is wet around my porch. Is she dieing or something? I can't really take her to the vet because if I try to pick her up she runs off. I went inside because I don't want to get whatever that is all over me but I left out a bowl of water and some cut up cheese/bread for her to eat, She also ran off after I made some movements and just stood there starring at some bugs when I tried to call her. She acted deaf, weird, and was slobbering like crazy! Is there anything I can do to help her? Like I said I cant take her to the vet, it would be VERY hard to because she would run away from me. I've grown attached to her and I would be very saddened if something happened. Please give me helpful suggestions.