If the government can stop the flow of cash by going fully cashless, then they can equally stop the penetration of bitcoin because bitcoin is also cashless and a lot of people will have to concert to Fiat before having to spend their earnings from bitcoin which still goes back to the point of running away from cash in first place. However, the way out is to find someone who is willing to buy bitcoin and pay cash or willing to trade bitcoin for his goods below the radar otherwise, I don't see a way out of the scenerio.
