Side information is being used extensively to improve the effectiveness of sequential recommendation models. It is said to help capture the transition patterns among items. Most previous work on sequential recommendation that uses side information models item IDs and side information separately. This can only model part of relations between items and their side information. Moreover, in real-world systems, not all values of item feature fields are available. This hurts the performance of models that rely on side information. Existing methods tend to neglect the context of missing item feature fields, and fill them with generic or special values, e.g., unknown, which might lead to sub-optimal performance. To address the limitation of sequential recommenders with side information, we define a way to fuse side information and alleviate the problem of missing side information by proposing a unified task, namely the missing information imputation (MII), which randomly masks some feature fields in a given sequence of items, including item IDs, and then forces a predictive model to recover them. By considering the next item as a missing feature field, sequential recommendation can be formulated as a special case of MII. We propose a sequential recommendation model, called missing information imputation recommender (MIIR), that builds on the idea of MII and simultaneously imputes missing item feature values and predicts the next item. We devise a dense fusion self-attention (DFSA) for MIIR to capture all pairwise relations between items and their side information. Empirical studies on three benchmark datasets demonstrate that MIIR, supervised by MII, achieves a significantly better sequential recommendation performance than state-of-the-art baselines.