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.
I think if the internet goes down it will really a big problem to all bitcoin users, traders and investors. It will also have a negative effect in bitcoin industry and community. I hope internet will never go down because it will also affect the price of bitcoin and there is a chance that the price of bitcoin will dropped to $0.