Hello Sally,
Chez-Git adopted a cat like that many moons ago. Poor little thing just jammed hesrelf into the tighest darkest corner she could find anywhere in the house and stayed there.
With the aid of an industrial size barrel of KY jelly and a crowbar (almost literaly) we would jemmy her out and force her to be petted from time to time.
Took years for her to get used to the idea that being petted was actualy enjoyable. Years more before she would offer herself up for petting voluntarily.
Not sure if any differences twix cat and dog and 'physchology' which make that a bad idea for petrified pooches ..
I am pretty sure that most of you know better than this, but for the benefit of anyone who happens across this post who doesn't, I am going to say this:
The absolute wrong thing to do with any animal who is afraid of you/doesn't want contact is to force yourself on them.
This is more vital the less domesticated the species is and the more afraid the individual animal is.
This means it's more important to not force yourself on an unwilling cat than it is to force yourself on an unwilling dog. The dog may bite you, but the cat will suffer more emotional trauma. And it's more important to not force yourself on a parrot than it is to not force yourself on a cat. Dogs are more domesticated than cats, and parrots are not domesticated at all.
If you want to quickly *tame* a feral or terrified cat (the two are not the same), this is a method I have used with great success:
Take all of the furniture out of a small room, except for a mattress put on the floor. The point of this is so that the cat will know that she is safe not because she's in hiding (because she has no place to hide), but because you are no threat to her. Enter the room only to provide fresh food and water, scoop the litterbox, and sleep. Never look at her, never approach her. Just come in, lie down, and sleep. Kate, who ended up being my best friend for eighteen years, was rubbing up against my ankles by the end of a week, even though it was some time after that before I bent down to touch her.
I don't normally do that; my normal method with ferals is to make sure that there is some place in the house where they feels secure, and then I go about my ordinary business. I am careful to pretend not to see them when they do start coming into rooms where I am, and I never, ever, look at them directly. (Looking at an animal directly is predator behavior if they don't know you and don't feel 100% safe with you.) Doing this, I've had ferals flop at my feet for a tummy rub within a couple of months. It's an individual thing - Ayla lived with me for five years and didn't want me to touch her until the end, when she was dying of cancer and found my touch comforting. Matilda currently sleeps cuddled up against me in bed, sometimes shares my pillow, but still doesn't want to be touched otherwise.
With all of them, I could use the bare room approach I described above to hurry the process, but it's my inclination to let them do it at their own pace. A matter of respect, you might say.