Retirees absolutely pay income tax. Withdrawing from a traditional IRA/401k generates ordinary income at the current federal tax rate. And any capital gains is taxed (albeit at a lower rate) when sold. It's a fraction of what they likely paid during their career, but it is not nothing.
Depending on the country of retiring, this could have majority tax implications. It's a big reason why people choose to retire in certain states: additional income tax on retirement income is possible, depending on the state.
Even if not zero, retirees' income is much lower than working people on average, and that income is taxed at lower rates. Further, tax paid to the US doesn't help the retirement country.
If they're residing in the other country, they're supposed to be paying income taxes to that country, in addition to taxes to the US. The taxes to the US will probably be canceled out by the tax exemption they can claim for the taxes paid locally though, but they still have to file in the US unless they renounce their US citizenship.
Very few people pay income taxes to a foreign government that they reside in unless they are actively working and collecting a paycheck. A passive income stream such as collecting social security or a pension is very rarely taxed. Even things like collecting rent as a landlord back in the home country or earning interest on a savings account there, are also very rarely taxed.
Then they're cheating on their taxes, and that government should probably look into how that person can afford to stay there with zero income. A lot of countries have tax treaties with the US to cover this sort of thing.
Depending on the country of retiring, this could have majority tax implications. It's a big reason why people choose to retire in certain states: additional income tax on retirement income is possible, depending on the state.