Each foreigner when arriving to the United States must have a passport, visa and arrival/departure records (Form I-94) to prove their status in the United States.
Sometimes it happens people may lose their passport or other documents, and to avoid further problems, it is better to always make a copy of passport biographic page, visa and Form I-94 right after your arrival.
If you didn’t get to make copies and lost your documents, you allowed to reside for the duration of your authorized stay, which is indicated on your admission stamp or paper Form I-94, Arrival/Departure Record.
If your Arrival/Departure Record was lost or stolen, there are few steps should be immediately done to replace it. First, you should report to the police about this loss. Again, it is better to provide a copy of a lost document, and police will issue a report about this accident.
Then you have request replacement of a lost or stolen Form I-94 by filling a corresponding application, that you can find on U.S. Citizenship and Immigration Services (USCIS) website.
Do not forget that you can always consult the local embassy about how to replace lost or stolen passport/visa. If you cannot contact or find the embassy, search for contact information online, as most countries place it on the embassy website.
The email to the Consular Section at the U.S. Embassy or Consulate outside the United States should include information about the state, where your passport/visa were lost or stolen, your name, date of birth, place of birth, address in the United States, and an e-mail address. Also, send copies, if it is possible, or at least the number of your stolen passport.