In The Prisoner, what happens to the Number 2 that is replaced?
Flushed out and send to the Village.
If it’s brown, flush it down…
I knew someone would take the bait. But a simulpost! 
Seriously, though…
The one who gets replaced after CHIMES OF BIG BEN returns some time later for another go-round in DEGREE ABSOLUTE, right? (And all while making clear that he’s the same character, not merely the same actor?)
I always imagined that each Number 2 was rotated back to the position he or she came from. Obviously, Number 2 worked for whoever was in charge; it’s not unreasonable to assume that he or she would be seconded to the Village for a time, especially if the person was a specialist in some sort of process or technique that had proven useful in the past. If they succeeded in getting Number 6 to reveal the reasons for his resignation, great; but if they failed, they simply went back to their regular jobs.
Remember there was at least one Number 2 who returned (Leo McKern), and IIRC, there was one other also (though offhand, I cannot remember who).
Although “Degree Absolute” would make a good title for that episode, it’s actually named “Once Upon a Time” (episode #16). But yes, it’s the same Number Two in both.
Yes, Colin Gordon, who was Number Two both in “A, B, and C” and “The General”. I believe he and McKern are the only actors who repeated the role.
In general, we never know. Probably nothing special, like what Spoons suggests. In a few cases (“Hammer Into Anvil”, “A Change of Mind”) it’s strongly implied that the Number Two meets an bad end — but that’s only implied, and we don’t really learn their fate.
I always assumed that the whole show was an allegory for a guy that went stark raving paranoid schizophrenic.
I believe is is as Spoons said; but as you say, it’s rarely clear. In ‘A, B, and C’ it appears that Number 2 met a bad end. At least he was set up for one.
He certainly seemed to be — though he then returns in “The General” with not a scratch on him. This rather undermines the tension in “A, B, and C”, retroactively, at least if one cares about continuity. (Probably best not to do that then, when watching The Prisoner.)
So maybe the whole series is a dream? Kind of like Newhart?