I talked about a similar topic a while ago, you may find this useful: https://forum.solidproject.org/t/authenticating-offline-first-solid-apps
As others mentioned, it’s not easy to know if a user is online or not. I like how Jake Archibald explains it in this presentation when he refers to this as Lie-fi.
But I think the issue with being offline is not about logging out, is it? If you’re offline, I see no reason why the authentication library wouldn’t be able to log out. After all, the library doesn’t store the token anywhere and requests it again after every refresh. So any data that the library is storing should be removable without an internet connection. This would be a different story if upon logging out you wanted to log out from the identity provider as well, but with the current implementation that’s not possible anyways (as Jeff mentioned).