Consider the situation: you're a dual US / Dutch citizen. You want to avoid paying US income tax (or just to avoid filling in a form each year that results in the IRS telling you that your tax bill is $0 because the Netherlands' tax rate is higher). But the State Department's renunciation route takes 3-4 years. So you mail them a letter instead announcing that you are renouncing your citizenship, and you include your US passport with the letter. You don't send the IRS a tax return in subsequent years, and you tell all your banks that you are not a US citizen and ask them to update your details accordingly.
I assume that what happens next is that your bank has a procedure for asking the US State Department if you have renounced your citizenship, and they say "no". So the bank continues to treat you as a US citizen, with all of the reporting obligations that entails.
Your method of enforcing this would (I assume) be to file a suit against the bank in the Netherlands and seek an order to prevent them from passing any information on you to the IRS. You would effectively be asking a Dutch court to rule on whether you can unilaterally renounce US citizenship.
I have never heard of such a case (either in the Netherlands or elsewhere), so I assume this has never been attempted. I don't know if that is because there is a strong reason to suspect that it would fail.