While in offline mode, if you open the asset store you get a message saying basically that you are in offline mode and cannot access the asset store, but you can still import previously downloaded packages into your projects.
The problem is, and I am probably just having a ´duh´moment, but there is nowhere to actually navigate to your previously downloaded assets. The screen for the store is just that one quick message, and no other navigation buttons. In previous versions of Unity, while in offline mode, there would be a long list of your assets with an ´import´ button next to each one. In Unity 5, nothing is listed, it is just an empty grey box.
Browsing assets that you already have downloaded is a barely tolerable experience in the Unity Asset Store when it is online, and when it is offline, it is useless because you cannot even use search. It has been that way for at least four (4) years, which is absolutely amazing.
This apparently-new twist of simply showing a blank grey box when offline (I see that too on my Unity 5.2.1) seems to me be just the natural progression of uselessness of the Unity Asset Store’s browser, and I doubt it will be changed anytime soon.
I recommend browsing directly into your filesystem to retrieve the files that you have. On Mac it is located under ~/Library/Unity (the ~/Library subdirectory is hidden by default; Google to unhide it) and it is located elsewhere on Windows; again, Google it up. From there you can directly drag the .unitypackage files into your project and keep working offline.
Ok, thank you very much. So it isn´t just me, it appears they removed the actual functionality in Unity 5.2. Currently living in a 3rd world country, and the last month my internet connection has been abysmal.