We study the flow and clogging of soft particles: micron-sized oil droplets, centimeter-sized hydrogel particles, and simulated soft particles, all draining out of a funnel. We find that softness is a key factor controlling clogging: with stiffer particles or a weaker driving force, clogging is easier. Softer particles form less stable arches and thus reduce the probability of clogging. We also study situations where single small droplets split into two or two droplets merge into one. The results have implications for oil droplets flowing through porous materials such as soil, where droplets can clog, break, or merge.