Calcium Chloride does not "react" with HCl. Calcium chloride is a water soluble ionic salt formed from one Ca+2 cation, and two Cl-1 anions. When CaCl2 is combined with water, the ions dissociate as they dissolve in the water.
Likewise, HCl, a covalently bonded gas, when dissolved in water, forms H+ and Cl- ions.
So when you combine CaCl2 and HCl in an aqueous solution, you end up with a mixture of Ca+2, H+, and Cl- ions in water.
None of the ions disappear, or go away. The compounds simply dissociate.