Imagine an RSS reader (which Facebook, Twitter, etc. basically are.) 99% of the time, an RSS reader doesn't need internet connectivity; it just has a database of synced feed-items and you can peruse them. When you pull-to-refresh it, it goes online and actually retrieves updates for its feeds, then (crucially) finishes and is now offline again.

There's no reason such an app can't be implemented as a plain-old-webapp pinned to your iOS springboard or whatever else. You open it, you get RSS items. You try to refresh, it says "no internet, sorry", and the refresh is cancelled. Every other part of the functionality continues to work just fine.

There's actually something that does exactly this: visiting the Gmail website on iOS will build a local database of your mail, and let you continue to interact with it, search through it, write emails and "send" them (they stay in your outbox) when you don't have internet connectivity.

It might help to think of this paradigm as "streaming apps". Instead of downloading apps and having them on your home screen, you go to a URL and it behaves like any other app--it will render its own app shell and then say "Sorry, can't get content. Check network connection".