My family recently (~3 months ago) took in a feral cat. They are fine with having an aloof cat that doesn't play or let you pet them, but they would like to do everything they can to make the cat comfortable and it would probably nice to be able to do those things if possible.
The cat is ~7 years old, was living in a hut outside, and was being fed by a neighbor until this winter. We are pretty sure he is completely or nearly completely deaf. When we met the cat outside by his hut he seemed perfectly tolerant of humans. He didn't run back in his hut or seem anxious with four people standing right by him, but he didn't react positively either. He is very cute, so my family figured it would be ok to take him, and he'd probably warm up over time. (When I was growing up my parents had a very aggressive feral cat around the same age, who softened up after about 5-6 years.)
So my family agreed to take him. The local cat rescue group trapped him. They took him to the vet who said he was aggressive and obese. The rescue group then held him for about a week, despite my family's requests to get him sooner. Once he arrived they kept him in a cage for a week. The rescue group suggested a week to a month, and my family took the minimum route as he had already been held in a cage for a week prior to arriving and it was starting to feel cruel. Once he was released from the cage he found a spot behind a bed to hide, which has historically been a favourite spot of cats. Once out of the cage he seemed to improve. He began pooping regularly, which he had not been doing in the cage, and he stopped having violent fits.
He stayed behind the bed for about a month. He would come out at night or when he believed no-one was in the room; the moment he realized someone was there he would jog back to his spot. Eventually my family had to move the bed out of that room. (It had to be moved and my family wanted to clean his spot, since it was becoming a source of smell (not urine) and they were concerned the amount of kibble he had brought back would attract insects.) We set up a new spot we thought would be nice by placing the hut he had been living in outside under a table and covering it with a table cloth. We provided one edge so he could see out the window (he had liked this when he was in the cage), and we placed it next to a radiator, since cats seem to like those. We moved his food there and gave him a couple days to move, which he did not. When it came time to move I pulled the bed out opening his spot up, and he jogged over to the new spot without much fuss.
He has been at the new spot for a little over a week, and he seems to have regressed a bit. He doesn't come out as much as he used to. He only seems to come out is to sit in a cardboard box we placed beside his spot, to eat, and to use the litter box on the other side of the room. Whenever he sees a person he runs right back to hide in his hut.
My family has been considering letting him out of the room to explore the full house, but is worried about his progress so far. They would like to do what's best for the cat and hopefully get him to be less afraid of people.
What steps can we take here? I've probably included a lot of unnecessary details here, and I certainly could include more, but I don't really know what is relevant.