The reality is that as a U.S. citizen you must file income tax returns even if you live in a foreign country. Some people don’t bother, but they can be subject to severe penalties if caught. Depending on where you live the tax treaty rules can be rather complicated.
And as far as estate taxes, many countries have treaties with the U.S. regarding who gets to tax the estate or portions of the estate.
It is not so easy as moving to another country - pay less tax. I have lived for several years in Europe, and I’m tired of being subjected to two very different tax systems. I expect that I pay quite a bit more in taxes as a result, even with various credits and exclusions. It is really extraordinarily complicated. I am eager to go home.
Since I plan on living in India, the IRS says as long as I make less than USD$17,900 per year, I don’t need to even file. That translates to over 800,000rupees/yr, which is a comfortable standard of living there.