Calcium chloride is deliquescent, it is hygroscopic, so much so that it dissolves in the water it has attracted by hygroscopy.
Sulfuric acid is hygroscopic, even if not anhydrous. So a solution containing water can be hygroscopic.
Is a concentrated solution of calcium chloride that was created by the solid salt attracting water still hygroscopic, attracting more water?
If yes - down to which concentration is that the case?