Microfluidic devices can successfully produce highly uniform emulsion droplets that are tens of microns in size. Smaller droplets are more difficult to produce due to geometry limitations. We have recently shown that micron-scale droplets can be generated via a tipstreaming-like phenomenon that occurs in microfluidic flow focusing devices when soluble surfactants are present. In this mode of droplet breakup a thin thread is emitted from the tip of a conical interface following the pinchoff of a larger droplet. The thread breaks into discrete, micron-sized droplets. The process is periodic, enabling continuous production of tiny droplets. The thin thread stretches affinely with the centerline velocity downstream and its lifetime depends on the velocity of the outer liquid, the viscosity ratio, and the surfactant mass transport properties. In addition, we observe that the cone angle from which the thread is drawn is relatively insensitive to viscosity ratio and surfactant properties. We describe a simplified model for the process that we have developed based on an observed symmetric corner flow in the inner liquid during the formation of the thread.