1. It could be an electric signal, in which case the most common thing to fail in the organ is the relay that opens and closes the valve.
2. It could be a pneumatic signal: the keypress opens a valve to let air through to a tiny tube which opens the valve on the music pipe. This was surprisingly reliable, but I'm slightly biased because a few decades before my apprenticeship, a slightly idiosyncratic pipe organ builder had been operating in the area, and he was a passionate believer in the goodness of pneumatics over all other technologies, so over his career he got very, very good at making reliable pneumatics. On those organs, it tended to be the tubing that would split.
3. Fully mechanical: you press the key to open the valve to let air into the pipe. The most stops you have open, the harder you have to press the keys. These tended to be much older instruments, so I saw a lot of holes in the bellows material.
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Other surprisingly common failure: birds and mice falling into the big pipes. Then they can't get out, and die in there. It gave a strange muted sound to that one note.
I did a handful of moves. It made sense when a church was moving to a new building, or some other "nearby" relationship, but for the most part it wasn't that much cheaper than buying one new. By the time you cushioned the pipes for transit and transported them somewhere else, you could have received an order from a factory for new pipes. The little tiny pipes are almost guaranteed to break or be deformed on a long move, and all the leather around the bellows will get torn.
The organ in the parent article is big. That's going to be a large job just moving it, and there aren't that many buyers for organs that big. (Because it will be expensive to maintain.) So they are looking for a major cathedral, a university's great hall, a big city town hall or something like that. All of which are going to struggle just to fund the work assembling the organ, let alone paying to buy it.
There was a requirement that the organ be kept together, which is why it is valueless. If they didn't mind someone buying it to fill up a spare parts supply, they could probably get some money for it.
The company I worked with didn't install into anyone's home, but one of our competitors did once.