For decades, travelers who were struck by disaster and lost (or forgot) their passport were usually able to have an emergency passport issued by the border police at their airport. I know several people who had their passport stolen a week before a long trip, but were able to have a travel document issued just 2 days before their departure.
The ability to travel to the US on an emergency passport has come to an end due to advances in technology. The United States demands that all passports of visitors arriving on the Visa Waiver Program contain a radio frequency ID chip with their biometric information.
Visitors from non Visa Waiver countries need a visa, and therefor always need a passport, so the ability to travel on an emergency passport never applied to them.
Sadly, nobody has figured out how to embed one of these RFID chips in last minute travel papers, so anyone who loses their passport is now up poop creek without a paddle. Since the US has no intention of creating an exception to their RFID rules, people without a passport will have to go through the process of getting a “real” replacement before they can head towards the United States, and in many cases will have to cancel or delay their travel plans.
The good news is that the United States is the only country that requires an RFID/biometric passport, so travelers heading to other countries will be fine.