What happens if I clear game cache of my last shelter survival?

Nothing major. Cache is just temporary storage of game files. You will not be logged out, lose any progress or items.

The game uses cache to store some of the minor settings. The most noticeable thing you will see is that your chat will be temporarily cleared (but will typically refresh after a few seconds). You will also lose some of your older mail, but recent mail will remain.

Bottom line - clearing the cache isn't going to cause any harm to your game session. All saved accounts will remain. Only thing I would recommend is that you take screenshots of important mail just in case it gets deleted. Mail takes up the majority of your cache - I believe that 500 or so mail items are stored on LSS's servers and anything over that is stored on your device.

I cleared cache and lost all progress.