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.
Yeah if the internet goes down many companies not only Bitcoin would go down with it. The internet has become so important in today's world.
Almost nobody can live without it, at least I can't.
Internet is main media and information platform it's using eveyware so bitcoin it's just a part of it and when internet goes down it will be just useless.