Soap and detergent solutions are used to wash clothes which are hypertonic* in nature as compared to the skin cells. This results in exosmosis in the skin cells and thus the skin over the fingers shrinks when we wash clothes for a long time.
*Hypertonic solutions: In hypertonic solutions, the concentrations of dissolved solutes are greater outside the cell resulting in the low concentration of water outside. Thus, to maintain an equilibrium, the water will flow from inside to the outside, causing the cell to shrink.