Droplet pinch-off of fluids with liquid crystalline order is a common yet poorly understood process. We report on measurements of pinch-off dynamics for a lyotropic surfactant/water solution in the lamellar phase and a thermotropic liquid crystal in the smectic phase. We find pinch-off is universal and well described by a similarity solution for a strain thinning power-law fluid. This finding is consistent with bulk rheology measurements which show these materials shear thin with the appropriate power-law dependence. Remarkably, we find depending on material processing, this universal pinch-off cuts off at different length scales. Collectively, these phenomena lead to an exceptional form of singularity where pinch-off is both universal and dependent on initial conditions. © 2010 The Royal Society of Chemistry.