As popular as the theology is, there is nothing in the Bible about a one world government or one world currency. That is a popularized fiction from the dispensationalist camp.
Although the anti Christ is given considerable influence over this world as a world leader, he never institutes a universal government. In fact, the prophets show that eventually there are pockets of resistance from the nations against him. Even the fallen kings of this world will think him too big for his own britches.
The mark of the beast is not a form of currency. It is simply a mark. In the Greek , it literally means to be branded like cattle (with a hot iron). The mark will simply be a form of identification showing loyalty. It is not a computer chip or any other such Hal Lindsey type theory.
As far as currency collapses, through the history of the world, currencies have always collapsed. Monetary systems are very fickle things, and all have never lasted a very long time. Even "the gold standard" that so many people seem to love had severe limitations and was very unstable.
Currently all the nations of the world have embraced a form of money known as "fiat" currenncy, which comes out of the "fractional reserve banking" system. It is entirely a debt based system of currency, where we trade debt based instruments known as "notes" with one another, representing our labor, time, goods, and services. It has "value" so long as our government says it has value. The purchasing power of these notes is highly dependent on other nations recognizing the value of our notes against their own, and the "value" or "purchasing power" of that money varies depending on how much currency is in circulation, and what other nations are willing to exchange their own notes for ours.
Eventually this will collapse when the ability to pay debts back collapses. This has happened already in smaller nations, whose ability to pay back debt has been crushed through hyper inflation, or whose nations simply take on debt loads that their GDP levels can't keep up with.
This form of system is pretty stable, so long as the wheels on the bus keep going round and round. It is a system ultimately designed for stable and secure nations, who assume their nations will be rather productive ones. Should anything cause production to slow down or come to a sudden hault, the integrity of the system is threatened. It presumes a normal life cycle of buying, saving, and taking out debts in order to keep going.
It is especially dependent upon debt to keep on going. Such is why the government never really educates the masses on personal finance in public school. They need you to be as ignorant about debt as possible, so you take on as much of it as you possibly can afford, and buy the biggest home possible, otherwise if most people failed to do such, it would collapse the system overnight if everybody simply paid in cash instead.
Such is partially why Fannie Mae and Freddie Mac were created, so that people could afford to take on high levels of debts that they simply were not loaned prevoiusly. Banks usually gave mortgages for no more than 8-15 years prior to the creation of these two housing giants by the government. It was simply too risky to loan somebody money for 30 years of their lives. Your local bank couldn't afford such risk, it wasn't profitable enough for them.
But such lending practices made for a weakened economy. As a result of all these things, these enterprises were created by the government so that the government would purchase such loans in mass from the banks, and thus, assume most of the lending risk. And such has been mostly a good thing for the government to do, so long as unemployment is kept low. Thus, America experienced a major housing boom for a few decades, with now 60%+ of adults owning a home instead of renting.
To show the weakness of our system, I have heard it has been said if everybody in our nation started using Dave Ramsey's financial philosophy, and lived debt free lives, the entire system would collapse over night. Money would have almost no value, as there is no debt upon which to issue notes, except for perhaps bonds issued by the government through the treasury department. A vast majority of the system depends on mortgages and auto loans to exist. Mortgages especially. As for every dollar paid into the banking system, 100 more dollars can be loaned out to others. Such loans are used to finance the creation of homes and businesses. And so the cycle repeats itself, more money comes in from savings and mortgage payments, and even more money goes back out into the nation.
So, if anything would ever weaken our appetite for consumer debt, such as a major catastrophic natural disaster, war on national soil, terrorist events, and things that lead to excessive personal debt obligations that we default on, the present system would collapse. Of course, when such seems to happen on a national level, such as in Greece, it looks like the solution to this problem is just to declare national bankruptcy, and essentially restart the system all over again.
So, there does seem to be some resolve in the system in the event of a collapse, at least, in regard to small nations. But we have yet to see what happens if a major nation is forced into bankruptcy, or lost it's entire interest in taking on additional debts. However, the "housing crisis" of 2007-08 in America, and the massive wave of defautls experienced on consumer debts, and the impact it had on America's economy ultimately caused a major ripple effect throughout the globe.
If for some reason our nation collapsed, it would cause the rest of the world to collapse overnight. The only way this collapse could probably resolve itself is through a massive series of world wars, probably only resolvable by an anti-Christ type figure. Then again, maybe not.
**edited**