We had an adopted stray like that a while back ("Kibbee") - another female so ours was very stressed out.
Finally just took KIbbee out back and...
NAW! Just kidding! Put an ad in the paper - something like, Nice, spayed orange female cat, likes people, doesn't like other cats!
A nice older couple came and took them to their house where Kibbee had a nice home and ruled!
Anyone wants pics of KIbbee, let me know.