The protein chemist resuspends the cell paste in water with detergent. The cell suspension is mixed with small glass beads in a grinding mill to break open the cells. With the cell proteins now in solution, the glass beads and cell debris are easy to remove by centrifugation or filtration. Hydrophobic proteins tend to stick to other water hating molecules like grease sticks to a plastic bowl in the dirty dishes. Hydrophobic proteins tend to be repelled by salts and water.
HIC resin is like small grains of sand covered with a layer of fat.
Hydrophobic proteins, like Protein X, stick when the cell proteins in the water solution are pumped through the HIC resin. Most of the other cell proteins flow straight through to waste. The Protein chemist adds salt to the water solution of cell proteins to make hydrophobic proteins stick stronger to the HIC resin. The salty cell extract solution of cell proteins is pumped through a bed of HIC resin where hydrophobic proteins, including Protein X, get stuck. Other proteins are washed out with more salt water.