If your passport is lost or stolen when you are traveling overseas, report it to police immediately, then go to the nearest US embassy or consulate. Often, it's possible to receive your new passport within 24 hours.
If you lose your passport more than once, you may be carefully questioned when you request the second replacement. That is because the foreign service must constantly protect against attempts at passport fraud, both by U.S. citizens and non-citizens. People who commit passport fraud do so for criminal purposes, such as money laundering, drug trafficking, terrorism, or to enter the U.S. illegally.
So, treat your passport as the significant and valuable item it is. Always carry it directly on your person for maximum safety, not in checked luggage, in your purse, or in a carry-on, where it can more easily be lost or stolen. Manufacturers of travel products offer various kinds of passport holders that you can wear under your clothing. Even though very clever pickpockets can sometimes defeat this method, your passport is safer worn this way than carried in a bag that can be lost.