In decades of rescuing and working with feral cats, Miss Annie here was the prizewinner of challenges. She showed up at our condo complex in some sort of distress, getting close enough to doors/entryways to have neighbors come ask for my help, but so fearful/feral that for weeks I couldn't get closer than 30 feet of her. A month or two of leaving food and water but not being sure she was getting it, and I finally spotted her at a distance watching me. Another month and she'd get closer in increments. I began sitting at a distance while she ate, inching closer each day. Then the pivotal moment when she brushed against my leg, and I gently touched her. Of course I got the usual first hiss-and-dash, but she was back shortly and that week I was able to pet her. Since she chose to sleep in the road (I know, terrifying) and appeared to be deaf, when she began waiting in front of my building I finally put on gloves and grabbed her. Because she had had so few hard luck breaks (sarcasm), nature chose to give her a vestibular episode four days after being inside for the first time in her life. A brave vet (and brave cat) diagnosed the episode, gave her what he could via shots. She could no longer climb to safety so she had mama to herself in the bedroom, where she remained hidden for two weeks. I'd exhale when I heard her use the litter box (under the bed along with food, water, and a blanket) If I heard her venture out, I remained stiff as a board and tried not to breathe too loudly. Finally one night I heard her playing with something, and s l o w l y rolled it back to her. Connection made. It has been four months since that moment and she's out and about with the others, making herself 'ta home. The best advice I can give as far as teaching a deaf cat not to sharpen her nails on the couch is to lift her up by her chest to break contact. It hasn't worked yet, but I'm still hopeful. Annie gets extra latitude because I think she suffered some kind of a head injury before coming inside. She's 90% recovered from the vestibular episode - just a slight head tilt and an odd way of running that's adorable and doesn't seem to bother her at all.
In short, patience always pays off.