As far I know, the two types of cats with no tail are the manx and the bobtail cats. There is an excellent discussion of tailless cats at
http://www.messybeast.com/bobtail-cats.html
It's quite a thoughtful and insightful read!
There is also a good site that focuses on Manx cats at:
http://www.best-cat-art.com/Manx-cats.html
Both breeds and there is apparently a sub-breed in the bobtail category.
As much as the scientist in me dislikes the use of anecdotes, I do have a personal story about a cat with no tail. Our first cat when I was a child - named after Puff of the Dick and Jane elementary school readers - had a kitten we also creatively named Blackie (one can guess his colour, lol). Puff had began her life as a feral barn cat who adopted us. She was pregnant when she arrived and had just the one live kitten - the other was stillborn. Probably because of that, Puff was so overprotective of poor Blackie that she dragged him all over the house. Curiously, she lifted him by his tail and not the scruff of his neck and by the time he was about two months old, this poor little kitten was left with virtually no tail at all. He looked like a bobtail cat. In retrospect, one wonders why she did not carry him the in the usual manner? (Anyone have any thoughts on that or heard of or expereinced similar situations?)
And I have heard of and seen cats who've had - for one reason or another - usually injury or serious llness - had their part of or all their tail amputated.
So, any one of those or something entirely different may have happened to your feral??
Good luck in acquiring her? Often, rescue groups or even the dreaded pound will loan you a trap to help catch the kitty.