Okay, suppose a US citizen emigrates. What happens to all the money he’s put into the Social Security fund? Can he ask the government to give it back? I’ve always thought that the government was holding that money in trust 'til your reach retirement age. Is there any legal precedent for this?
No, the government isn’t holding the money in trust. They spend it pretty much as fast as they get it paying current social security benefits. The deal is not that you will get back your money but that, when you qualify for benefits, you will receive a benefit funded by the then current contributors to the system. The amount of the benefit will depend on the rules in place at the time, but it is unlikely to be related to the amount or value of the contributions which you have paid.
What happens if you leave the country? Depends where you go. Some countries have social security agreements, whereby each country recognises contributions to the other’s social security system. I do not know whether the US has any such agreements or, if so, whether they have one with the country you have in mind but, if so, then the emigrant’s expectation of receiving a benefit under the US social security system is replaced with an expectation of a benefit under some other country’s social security system.
If there is no such agreement in place, most countries simply preserve social security entitlements. So if you contribute for (say) twenty years and then emigrate at the age of 45, when you reach pension age you will receive the same benefit as someone who contributed for twenty years and then stopped at the age of 45 for some reason which was not emigration (e.g. they stopped working).
Costa Rico (and other countries) has a requirement that you have so much income in order to emigrate and for retirees this can be met by showing proof of social security payments. Social Security is figured on your 10 highest years of participation, which means you probably don’t have to work 20 years to be eligible.
USA has agreements with most other countries concerning Social Security Benefits. You don’t lose anything when you travel to another country if you remain a US citizen. In fact, your earnings in other countries will also contribute to your benefits due to these agreements.
Of course the government is not holding it in trust for you until you retire. If you become “disabled” (as that word is defined in the Social Security Act), you will be eligible for benefits sooner.
Check out this regulation and the following ones for provisions of these “totalization agreements”: http://www.ssa.gov/OP_Home/cfr20/404/404-1901.htm