Unless that particular farm is the US or North Korea. Both of which expect you to keep filing taxes on money you earn no matter where you earn it .
 Obviously there are exemptions for foreign earned income, but if you're in country with lower tax than the US (of which there are a fair amount) you could end up paying the US taxes on money that has literally nothing to do with them. Worse, if you're married to a native of that country and must file jointly in the new country then the US expects you to file jointly with them too and pay taxes on your spouses earning.
Yeah if I was from the US I would have to renounce my citizenship, but there's no doubt in my mind I would have done so if necessary. Also it's the US and some African tinpot dictatorship if memory serves.