It has been found that solubility at the Krafft point is nearly equal to critical micelle concentration (CMC).
The Krafft temperature is a point of phase change below which the surfactant remains in crystalline form, even in an aqueous solution.
Visually the effect of going below the Krafft point is similar to that of going above the cloud point, with the solution becoming cloudy or opaque due to the surfactant molecules undergoing flocculation.
Surfactants in such a crystalline state will only solubilize and form micelles if another surfactant assists it in overcoming the forces that keep it crystallized, or if the temperature increases, thus causing entropy to increase and encouraging the crystalline structure to break apart.
Surfactants are usually composed of a hydrocarbon chain and a polar head group.