If the internet goes down, Bitcoin is rendered useless, you pretty much can't do anything. But I doubt that the internet will ever go down, as in like fully shutdown across the whole world.
If internet goes down, it would be a great trouble for everyone who use it. Well bitcoin is a digital currency, meaning it will function with the use of internet. It will not work, and break down. But one thing I know is it won't happen that the internet goes down because we are now living in a modern technology.
Everyone will get affected by this since all of us are now relying on the internet, so I don't think that there is a government and a private company that can operate, people who are always watching news and updates in any social media will get pissed of and even banks, so I think it cannot happen.