In your example, which alliance does nothing in response, CIS, or NATO?

To cover all bases:

- CIS isn't a military alliance, so its prerogative isn't for its members to protect each other militarily. CIS without Russia would also be insufficiently large if it was a military alliance to defend any member from Russia.

- Russia has a history of invading the member states of its own alliances, like the USSR did to a couple of the Warsaw Pact states, namely Hungary and Czechoslovakia. The point of Russia's "alliances" tends to be to serve Russia's own interests, not those of the other member states. Its much more likely that NATO states are safe from each other, and from the United States.

- NATO doesn't want to fight a direct war with Russia in order to prevent a nuclear exchange, which is only sensible, but it is offering substantial support to Ukraine, or Ukraine would have already been conquered. The most that could be argued is that NATO isn't currently offering sufficient support for Ukraine to win the conflict. In any case, this is far from doing nothing. What it looks like when your allies do nothing, or less than nothing, was for example the Munich Treaty situation, when Czechoslovakia was effectively forbidden from defending itself from Nazi Germany by the western powers and Czechoslovakian territories were immediately annexed by Nazi Germany.