Could you give an example of how this works?

I know a couple of US-born people who have successfully relinquished their US citizenship, and were not made to pay any money to the US as they were not renouncing. One of them says she does not get hassled when entering the US (due to ignorance of the rules) because her place of birth is a place which also exists outside the US, and it is just listed as that in her passport. The other was born in New York and has not been hassled either but he tries to avoid travel to the US.

I think that if you want to relinquish your US citizenship because you genuinely do not have ties to the US and would only visit for the same reason as a regular citizen of your new country, then you should do so without worrying about problems entering as a tourist.

While, the link you provided does not specifically state that there are fees involved, it also does not state that there are no fees involved. I haven't looked at all the code sections referenced in the link, but I am highly suspicious that you can renounce your citizenship at no cost. And I do not really see any difference between relinquishing and renouncing. Have you discussed this matter with a lawyer?

As with those who have a work history with State's OLA, I have no doubts that some relinquishing of US citizenship involves no fees being due for relinquishing citizenship. I also have no doubt that the consequences for relinquishing US citizenship are not a perfect copy of the consequences of renunciation of US citizenship. About the above, I have no doubt that current or former legal and/or national security-related staff working on such matters for State or other parts of the USG have this understanding too.

I can't confirm the accuracy of the tax lawyer advice that was relevant to the following situation, but at least a couple of tax lawyers working for or commenting about Tina Turner relinquishing US citizenship made representations that the IRS/Treasury compliance consequences were different for a relinquishing of US citizenship than for a renunciation of US citizenship.

So, would it be useful to ask the people at the US embassy in Nicosia what the difference between relinquishing and renouncing US citizenship is and how one goes about either (though I think I clearly understand the renunciation process and associated fees and tax requirements)? Somehow I have my doubts they would have any answers for me, especially since they couldn't even correctly renew my US passport 2 years ago.

You can ask. However, IIRC, ACS and others at US Embassies/Consulates are generally directed to steer people to retain their own legal advisors on such matters. They do provide info about the consequences of losing citizenship but, for informational purposes, they don't generally segment the particular consequences by the various paths of losing citizenship (and consequently being recognized as having lost US citizenship) and go into the nuances of matters in this area. A big reason the costs for renunciation was jacked up because these loss of citizenship reviews go back to DC for more extensive legal reviews and because the volume of requests and work related to each request involving this have increased a lot.

Which is understandable, given that the 14th Amendment confers citizenship automatically upon anyone (with very few exceptions upheld by the Supreme Court such as foreign diplomats or hostile forces) born on US soil, regardless of the citizenship of their parents.

Of course that doesn't mean that people born here never renounce US citizenship.

The only way you "relinquish" US citizenship without cost is if you are discovered to have committed fraud in acquiring it in the first place, or the US government decides to do what they have never done once in all of US history, and persuade a court that you have committed an "expatriating act," such as serving in another country's armed forces. "Relinquishing" in these circumstances is not voluntary.

If you wish to voluntarily lose your citizenship, "renunciation" is the only option, and with the latest revision to the consular fee schedule, it now costs over 2500 USD. There is no way to request to "relinquish" rather than "renounce".

That's exactly the issue. The overwhelming majority of people with a U.S. birthplace are citizens, due to the US use of juris soli in the form of the 14th Amendment. The U.S., like most countries, also requires its citizens to use their US passports on entering the country, even if they have one or more other valid passports. Therefore an arriving passenger bearing a foreign passport specifying a US birth place would appropriately raise some questions in the immigration officer's mind. However, U.S. citizen born outside the USA who presented themselves at a port of entry with a foreign passport would not ordinarily raise such concerns.

They've done it more than once; Vance v. Terrazas in 1980 and Richards v. Secretary of State in 1985.

(Current policy and Action and Deltamar v. Rich (1991), are more stringent on the intent factor, but if you really mean to give up US citizenship then intent is clearly not the issue....)

Vance v Terrazas had the opposite effect, voiding laws that provided for automatic loss of citizenship, and establishing that citizenship could only be lost if that was the citizen's intent, whilst retaining some wriggle rom in the form of acknowledging that actions other than signing a form renouncing citizenship might form the basis for demonstration of intent.

Richards was a narrower case and in any event has been superseded by changes in both US and foreign policy. Canada no longer requires passport applicants with other nationalities to sign a renunciation statement, and US policy no longer seeks to use such statements as a basis for denying a U.S. passport.

So whilst in theory there are still other means to get rid of your US citizenship that don't involve a lengthy bureaucratic process and a 2500 dollar fee, in practice it's unlikely to happen unless you show up on YouTube beheading a western journalist whilst shouting "Allahu Akbar," in which case you're probably likely to lose more than your passport, and they may decide to let you retain your citizenship for the duration of your life without parole sentence in any event. Given the choice, most people, I believe would go for for the fee and form option, so whilst you are correct in the theoretical legal sense, in practice there is no alternative path to losing your citizenship other than renunciation.

Just curious as to what type of visa would be issued to the former citizen to allow them to turn up and ask for entry?

Well, in this case we're talking about a ptential Spanish citizen so it would be an ESTA and not a visa.

Often if you want to stand for public office then you have to renounce your foreign citizenship, eg this (US born) former Australian State Premier.

Yes, but it really depends on the nature of the trip and the details of the purpose. The U.S. does issue visas in the Spanish passports of Spanish citizens for a variety of reasons, not all of which involve an intent to reside in the US. Not all trips by visitors using a passport of a VWP country can use the VWP for admissibility to the US; and even if some such persons could use the VWP, some may not want to use the VWP.

Honestly, If I wanted to go back to live/work I would just get a green card. Seeing as how I have living immediate family in the US. I can also leave and give up the residency and fiscal requirements much easier.