What you are describing was a major problem for English finances in the seventeenth century. Most coins minted in England before c. 1680s were simply a hammered weight of silver. The hammer would stamp the coin with the seal indicating that the coin had a certain standardized weight, and would be traded at that value. However, since the coins were only hammered, the edges around the coin could be worn down with time or cut off the coin, so that the coin would only have half it's proper weight. This process was known as clipping, and it was an offence punishable by death. Clippers, as they were known, would shear the edges off of coins they had, and melt down the scraps into bullion, which they would typically export to the continent in exchange for hard currency. Then they would take their new foreign coins, have them minted and begin the process over again. They were not this straightforward as men making silver appear out of their ears would have been suspicious, but its a rough portrait.

Now the main reason we know this happened on a massive scale is because the English crown sought to fix their finances in the late seventeenth-early eighteenth century in what was called re-coining. The new coins would have stamps on both sides of the coin that take up the whole surface, and then the coin would be rolled giving it a definable edge that would stop clipping. If you look at a modern Quarter, it has the kind of edging found in the re-coining. What makes re-coining so interesting is that two of the greatest minds in English history were integral to the process - John Locke and Isaac Newton. Locke was a member of the board of trade, and wrote a famous piece on money called Further Considerations Concerning Raising the Value of Money. This is a difficult to understand work because we live in an age where inflation is normal, and we understand the idea that a dollar bill only represents money - it has no inherent value. I will try to explain briefly Locke's work:

In this work, Locke disputed that clipped coin could operate as an exchange as the value of the coin was lower because it had less silver. In his second treatise he wrote "gold and silver, being little useful to the life of man, in proportion to food, raiment, and carriage, has its value only from the consent of men." For Locke, silver only had value because it was admitted to have value - and it's value was directly related to its weight. Therefore it made no sense to Locke that a coin could represent more than its weight. Locke on Money became the gold standard of Economic works for nearly a century until Adam Smith came along to explain represented value and real value.

So, Locke claimed that the currency in circulation had to be the actual amount of silver in circulation. Sir Isaac Newton agreed with Locke, and as the Warden of the Royal Mint, began bringing in coins, melting them down, and reissuing them at the proper size and weight. This caused a huge problem because, as it turns out, the coin circulating in Britain was operating at double its value. In other words, the coins had been clipped and worn so much that a silver pence had the silver weight of a half pence. There was massive deflation as the amount of currency in circulation was cut in half over the course of about 25 years. Looking back the problems of inflation and deflation are obvious, but to the people operating under Locke's arguments the deflation was a near impossible problem to understand.

Sources: Westfall, Never at Rest; Woolhouse, Locke: A Biography; Cranston, John Locke: A Biography; Appleby, "Locke, Liberalism and the Natural Law of Money," Past & Present 1976, pp. 43-69.