To my greatest knowledge, if the internet goes down, my bitcoin asset is also going down because the internet has been a networking system that authorizes accessibilities to my wallet so that I can utilize my funds.
You said we can access our bitcoin without internet, please I'll be interested to learn about this possibilities.
If the Internet suddenly stopped working globally, the value of Bitcoin and other cryptocurrencies would theoretically be unaffected, as no one (or very few people) would have access to their funds. Only satellite networks and some military networks, which always operate in isolation, would continue to function with some normality.
At that point, with all the chaos and problems that all countries would have, the value of cryptocurrencies would surely be the least important thing at that time for the population. Health systems, for example, would be the most affected, and probably also the defense systems of less advanced countries that do not have isolated networks or satellites.