Good question, there are many factors to consider.
What country was the passport issued by?
What country are you in?
Does the country that issued the passport have representation in the country where you lost the passport? Does it have an agreement with another country to act on its behalf?
I know a person who lost a PNG passport in Cairns and received a special travel pass to return to PNG on the same day as the passport was lost but I would imagine losing a passport in outer Mongolia would be a lot different to that scenario.
The first thing I would consider doing is reporting the loss to the local police and get some form of "official" report from the police.