In the real world you could look at Nauru, which was a very low tax money laundering haven in the specified time frame. Though its a very small country with an interesting history.
The reaction of other states probably depends on how big of a problem that state is in the grand scheme of things. When the money laundering is too severe at some point international alliaces will impose sanctions, cutting of money tracks. For that to not destroy the countries economy, they would need powerful external friends. Probably some kind of world powers, that hold a protecting hand over them for geopolictical strategy.
Also: In such a place there would be people from all over the world, even the big world powers, doing shady bussiness. For the secret agencies of big countries such a money laundering haven can be a good opportunity to pipe money to some cronies. Think of the CIA financing groups of terrorists/militias to disturb a too socialist country, or even bringing its government to fall and be replaced by one doing the US favors (Osama bin Laden comes to mind).