How do you re-enter the US from Mexico or Canada if you lost your?
If the said passport is a US passport, they should take you to the 2nd level interview, where you will be asked many questions about yourself, your family, your work, to ascertain, you are actually you, not an impostor. Then they will contact the necessary departments and get a copy of your passport and other relevant documents to compare your picture to your face. etc. Then they should allow you in if everything checks out. If you are foreigner, you need to contact your embassy or nearest consulate in these countries and get a replacement passport. Then contact US consulate and explain what happened. They should be able to help you with the US visa.