We study the micellar solubilization of three thermotropic liquid crystal compounds by immersing single drops in aqueous solutions of the ionic surfactant tetradecyltrimethylammonium bromide. For both nematic and isotropic drops, we observe a linear decrease of the drop size with time as well as convective flows and self-propelled motions. The solubilization is accompanied by the appearance of small aqueous droplets within the nematic or isotropic drop. At low temperatures, nematic drops expell small nematic droplets into the aqueous environment. Smectic drops show the spontaneous formation of filament-like structures which resemble the myelin figures observed in lyotropic lamellar systems. In all cases, the liquid crystal drops become completely solubilized, provided the weight fraction of the liquid crystal in the system is not larger than a few percent. The solubilization of the liquid crystal drops is compared with earlier studies of the solubilization of alkanes in ionic surfactant solutions.