One crucial question facing European Union governments right now is whether it's possible to have a partial breakup of the eurozone. Could Greece exit (or be kicked out) without that creating uncontrollable panic in Ireland, Portugal, and Spain, leading to the dissolution of the whole thing?
I asked on Twitter for historical examples of partial dissolution of currency unions, and there aren't a lot of encouraging precedents. In part, however, that's because currency unions are rare. Let's start with some non-examples. A few people suggesting the Austro-Hungarian Empire, Yugoslavia, or Czechoslovakia as precedents. These, however, point the other way. When they fragmented, they fragmented all the way down.
Justin Fox offered the United States at the beginning of the Civil War, but I also think that goes the other way. Obviously it would be a mistake to say that the war was "about" the stability of the national currency and banking system, but it is certainly true that one reason the principle of the indivisibility of the Union was more popular in 1860 than was Abraham Lincoln's anti-slavery platform is that people didn't see where the limiting principle would be. Either the United States was a single sovereign republic governed by the terms of the constitution or else it was a loose and perennially unstable collection of sovereign entities that might back out anytime things didn't go there way.
I would also put the interwar Gold Standard in the category of total dissolutions of a currency regime. The Gold Standard "worked" as a monetary system as long as it was "unthinkable" that a country would abandon gold. But once countries started leaving, there was a downward spiral.
Alan Beattie perhaps has the winner, citing the Sterling Area of the British Empire and Commonwealth. This was a bloc of independent or semi-independent countries that either used the pound sterling as their currency or else pegged their currency to sterling. Canada and Newfoundland (which was independent for much of this period) never joined up, feeling that their economic fate was more tied-up with the United States. But countries managed to leave after political or economic changes. Egypt left in 1947, Sudan left in 1957, Iraq left in 1959, Rhodesia was kicked out in 1965, but the thing kept rolling until a gradual unraveling in the early 1970s. So it's not inconceivable.