In such cases, distributional initialization makes the learning task easier since in addition to the contexts of the rare word, the learner now also has access to the global distribution of the rare word and can take advantage of weight sharing with other words that have similar distributional representations to smooth embeddings systematically.
distributional initialization is a form of smoothing: the embedding of a rare word is tied to the embeddings of other words via the links shown in Figure 1: the 1s in the lower "rare words" part of the illustrations for separate and mixed initialization.