Depends. We have gigantic (like swimmign pool sized) tanks filled with brine for our big stuff. The brine is essentially like whey at this point. We don't change it, it has an in line filtration system and we have a management plan for keeping it clean. You wouldn't be able to dump and remake tens of thousands of gallons of brine every week.
With that said, some operations brine feta seperately in tubs so they can use different brine conditions. The draw back to the gigantic tanks we have is you can't dose your milk with anything, or you'd be dosing EVERYTHING with it.