Some thought on the softener might help. Would it be logical to have a softener installed if the water is soft coming out of the ground? This would lead me to think the raw water is hard and they wanted it soft so installed the softener. Several hundred dollars and time/expense to keep salt in it so normally folks don't go that way for no reason.
On the salt issue, there is no difference how much salt is left in the brine tank as long as there is some. The water added to that tank will only dissolve to the correct point and should be set to allow enough brine water to use to flush the softener resin. I would guess the little blue tank might be totally sealed with maybe an air valve on it? That sounds like a small pressure tank to make the water flow while the pump itself is not actually running. A point for the owner to be aware of as it may occasionally need the air in the tank adjusted to keep the water flow steady. Not a big thing but something to be aware of at some point.
I would look for a raw water tap before the softener. Usually there is some spot to get raw water.