I wonder how Black Widow would react to her homeland dying
I think it depends on the comic continuity.
In most continuities, I could see her be saddened by her countrymen killing each other and that the attempts at reforms failed so miserably. Maybe Marvel tries to do a "is she going to betray SHIELD?" storyline but later it's revealed that she was stealing money and equipment to smuggle refugees out of Russia.
In Ultimate Marvel, where she was a traitor who sought to destroy the US because it "crippled and turned Mother Russia into a bankrupt nation of hookers and gangsters," I could see her double down on her hatred of the US.
In the MCU, at the time of the Collapse of Russia, Natasha would have been undercover in Ohio with Yelena Belova, Alexei Shostakov,and Melina Vostokoff while Shostakov and Vostokoff were tasked with stealing data from North Institute.
With the violent collapse and fracturing of Russia, who knows how this could have gone and who would "inherit" the Red Room.
If Red Room is inherited by the Soviets or the Nationalists, then Natasha's training would be the same but her assignments would be targeted at enemy Russian states. If Red Room is inherited by the Russian Federation in Kaliningrad, she could be in a position where she aids SHIELD against spies from the Commies or Nazis.
Edit: Adding "Natasha gets to grow up happy" timeline.
Or maybe Red Room collapses, allowing Shostakov and Vostokoff to take the girls and defect. They work for SHIELD and both Yelena and Natasha get to grow up as (mostly) normal girls.