The brine tank should always have at least 4 - 6 gallons of water in the bottom. It refills after the regeneration cycle so that the new water will dissolve the salt in time for the next regeneration. After cleaning the tank, you should have precharged it with enough water to be on hand for the first regeneration.
I would Google "brine tank does not refill" and "brine tank mushing" for diagnostic help. The Terry Love forum has excellent forum members, both pro and homeowner contribute there. There are numerous reasons, one simple one is just the fill tube clogged by salt bridge or the float valve was stuck closed. Maybe incorrect salt type? Tank should be cleaned annually?
With my softener, I like to only put about two bags of salt max (depends on brine tank size) and slope the salt to one side so you can observe the water line and keep problems at bay. My brine tank also has the tray on the bottom to assist preventing a salt bridge.
Brine tank bottom grid plates:
From a link in a Google search: "Mushing
.....If the salt in the brine tank is packed too loosely, the salt can change into small crystals. These salt crystals eventually start to bond with one another, creating a mass of salt at the bottom of the tank. This process is referred to as mushing. The mass of salt can block off the fill line in the brine tank, preventing it from refilling.
You need to clean out the brine tank completely and repack the salt properly to fix this issue. Different water softeners can use different kinds of salt and methods of packing. Make sure you use the manufacturer's suggested method when packing the fresh salt."