What happens if you overdraft your checking account and stop using it you are not a US resident and the only ID required to open the bank account was the passport from your country?

Doing so would be both a crime, for which you could be charged, convicted and punished by fine and/or imprisonment, and a civil offense, for which you could be sued in civil court for money damages. Depending on the amount the crime might be a misdemeanor or a more serious felony, determined by the applicable state law. If a felony, and if you are a resident of a nation with an extradition treaty with the US, you could in theory at least be subject to forced return to the US by extradition to face the criminal charges. Your presence would not be required for a judgment to be entered against you in civil court, which would then become a lien on any property your have in the county where the judgment is docketed. Depending on your nation of residence its possible attempts could be made to collect from your assets there. The unpaid overdraft would become a part of your credit history on the various credit reporting agencies, and would make it more difficult to obtain credit from lenders using information from those agencies in lending decisions, and would make it very difficult ever to open another account in the US until the defaulted amount is paid.