If you keep a couple focus icons on the Rancor (say via yoda), if after refresh the rancor still has 1 token, it's text does not come into play correct?
Rancor Text
It's ability still triggers. Page 27 of the rulebook:
exhausted
A card that is exhausted (i.e. has one or more focus tokens on it) cannot be focused to pay for card effects, cannot focus to strike, and cannot generate resources. However, other card abilities of an exhausted card may still be triggered, and its constant effects (if any) are still active, as long as such abilities do not require the card to focus, to be ready, or are not otherwise prohibited by the card text.
Important stuff in bold.