They start making special molecules that populate the tardigrade's cells.

It's thought that as water becomes scarce and tardigrades enter their tun state, they start synthesize special molecules, which fill the tardigrade's cells to replace lost water by forming a matrix. Components of the cells that are sensitive to dryness, like DNA, proteins, and membranes, get trapped in this matrix. It's thought that this keeps these molecules locked in position to stop them from unfolding, breaking apart, or fusing together. Once the organism is rehydrated, the matrix dissolves, leaving behind undamaged, functional cells.