We can see here that the chemical that is present in the sodium chloride solution that provides the hydrogen that's collecting at the cathode is the water.
In a sodium chloride (NaCl) solution undergoing electrolysis (such as in the process of electrolysis of water), the hydrogen gas collecting at the cathode is not directly provided by a chemical in the sodium chloride solution itself. Instead, it's generated through the electrolysis of water molecules present in the solution.
During electrolysis of water, water molecules (H₂O) dissociate into hydrogen ions (H⁺) and hydroxide ions (OH⁻). The cathode attracts positive ions (cations), which, in this case, are hydrogen ions (H⁺). At the cathode, the hydrogen ions (H⁺) gain electrons from the cathode electrode and are reduced, forming hydrogen gas (H₂).