So let’s say that I buy a home and a business in Costa Rica. I move there, maintain a dual citzenship, and run my contracting business. Do I owe anything to the US government?
The IRS will tell you that you pay US Taxes wherever you are, unless they have a tax treaty whereby enforcement is exchanged with the treaty nation then the tax is paid where you are resident for 6 plus months a year.
The chances of them catching you? well it depends on how you do it.
“So let’s say that I buy a home and a business in Costa Rica. I move there, maintain a dual citzenship, and run my contracting business. Do I owe anything to the US government?”
That depends on a number of factors. You would be well advised to speak to a CPA familiar with tax law in Costa Rica & the USA.