Say a wanted US fugitive goes into the US embassy in Moscow and gets arrested because he is setting foot on “US soil”. Could the US extradite him back to the US against the wishes of Russia? (they’d have to cross Russian soil to get him to the Russian airports, transportation, etc)
Absolutely not as witnessed by the Julian Assange affair:
The other way round, he was granted asylum by Ecuador in their UK embassy, but Britain was having none of it and there was no way to for the Ecuadorians to get him back to the Ecuador, so he was stuck in the embassy.
Logistical (and even in principle) I’m not sure there would be any means to arrest and hold someone in a US embassy, and even if it was, there would presumably be constitutional an issue with holding someone indefinitely until it was possible to get them back to the US for his day in court.
[[deleted by poster]]
This is a common misconception. A foreign embassy is not the soil of that country. It is still the sovereign soil of the host nation. Embassies have special protections under traditional international law and custom, and specifically under the Vienna Convention on Diplomatic Relations, but the U.S. embassy in Moscow is still sovereign Russian soil.
@griffin1977 points out one instructive high-profile case from recent years. Another high profile case from recent years was that of Jamal Khashoggi, who was murdered in the Saudi Arabian consulate in Instanbul. The assassins were not operating on “Saudi soil.” They were operating on Turkish soil, and subject to Turkish laws. Part of the reason they murdered Mr. Khashoggi was precisely because they couldn’t just arrest him and bring him back to Saudi Arabia without Turkey’s permission.
All of which is not to say that such renditions never occur, but they are extra-legal, and a dramatic abuse of diplomatic protections.