There are two variants here.

  1. People who have money in overseas accounts and their home government cannot do anything about it – because it is structured in such a way, that the local government’s taxation arm has no way of imposing collection on it.
  2. People who simply have money overseas and hide it, i.e. don’t declare it and don’t want anyone to know about it.

I presume you are talking about the latter.

Many countries provide a way (read: incentive) for external money to come into their country. They could do this through a stock purchase, etc. there is no getting caught scenario here, just that once the transaction has been realized, you might have to pay a tax on it – either now or at some later date (because the transaction is now part of the mainstream records).

Some bring it through off-shore debit cards that they continue to use in the country. Debit cards for money parked outside is one the largest methods of utilizing your money on a day to day basis.

It depends on who you are (person of interest?) and how much you are spending in the local economy that would be the government’s interest in pursuing your wealth abroad.

Contrary to popular belief, 100,000s of Americans store their wealth abroad, through various legal means and they have equally a legal way of bringing that money back into the US and spending it.

Likewise, many other countries also provide this luxury. Nowadays, bearer instruments is the preferred method, but that the chain of transactions have to be cash only.