I'm travelling in Taiwan, currently in a little village on the east coast with quite a few expats.
I just ran into one acquaintance from the US who tells me he thinks he's lost his passport.
Given that the US has good relations with Taiwan but does not have true embassies or consulates here, I'm assuming there must be at least a slightly different way to deal with a lost passport situation compared to being in a fully recognized country.
The US (as well as many other countries that do not have diplomatic relations with the ROC) has an embassy in all but name in Taiwan. It's called the American Institute in Taiwan (AIT). It is staffed with US diplomatic personnel like other US embassies, handles the usual embassy and consulate business like issuing US passports and visas, the "director" is paid the same as a US ambassador, and the website has the exact same design and style as websites of US embassies, etc.
(And conversely, the ROC maintains embassies and consulates in all but name in the US and other countries it does not have diplomatic relations with, called the Taipei Economic and Cultural Office (TECO, for consulates) or Taipei Economic and Cultural Representative Office (TECRO, for embassies)).
