Related news from NYT: 

Russia’s state airline, Aeroflot, said on Saturday that it would suspend all international flights from Tuesday “due to additional circumstances that prevent the performance of flights.”

[...] Separately, Russia’s aviation authority, Rosaviatsiya, recommended on Saturday that Russian airlines with planes registered in foreign jurisdictions suspend all flights abroad from Sunday because of fears that they could be seized by foreign governments.

The suspension effectively leaves a handful of Western companies with no way of recovering hundreds of planes leased to Russian carriers. [...] According to IBA, an aviation consulting firm, there are nearly 600 foreign-owned planes currently leased to airlines in Russia. Those planes are worth an estimated $12 billion, about a third of which belongs to Irish lessors.

Border could be closed as soon as Friday when the Federation Council hosts a special meeting. 
 

Here is a document (in Russian) with lots of useful information about emigrating from Russia right now.  I agree people currently in Russia should strongly consider leaving. I am reasonably optimistic that European/etc governments will open pathways for Russians to apply for political asylum or similar in the nearish future. At the moment, Republic of Georgia might be a good option as Russians have almost 1 year of visa-free residence there.