The U.S. Embassy is monitoring reports that extremists have imminent plans to target large gatherings in Moscow, to include concerts, and U.S. citizens should be advised to avoid large gatherings over the next 48 hours.
Diplomatic communications haven't totally broken down yet, it serves a great purpose in passing communications between the two countries. It's normal to keep embassies open as long as possible. Hell, in world war 2 the US even maintained their embassy in Nazi Germany up until 1941. It didn't do much at that point but it stayed open until we were legally at war and communicating didn't matter.
This is probably mostly addressed at people with dual citizenship or Russian ancestors and families, especially Jewish ones. They might count themselves safe from Russia itself, yet. But they could easily become branded as spies and demonized at some point. Not this time, that is more to do with Islamic extremism and probably actually a common concern of both US and Russia. Doesn't look good for Russia if Russian American Jews get killed due to internal issues with terrorism.