Ummmmmm
And an immigration visa.
Ummmmmm
And an immigration visa.
I knew one guy whose only legal requirement was to leave the country twice a year, for a day, in order to come back for another 6 months. But he didn't even do this - he went one step lazier and hired someone else to run his papers to the border and back every 6 months.
It's a country-by-country thing, and maybe they've closed some loopholes, but I'd be shocked if a wealthy American can't still get away with this in dozens of poorer nations.
Then you fly back to US or visit another country for a month and go back to your base country. You can do this with Visa-on-arrival at most countries with a US passport.
In the USA, if you don't seek employment and stay out of the 100 mile 'constitution-free' zone and live in a state that doesn't link the criminal justice system to immigration (I think California is an example) I think the chance of getting caught as an illegal immigrant are about zero unless you catch a felony or something.