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Semi-supervised classification-training both on labeled and unlabeled observations-can yield improved performance compared to the classifier based on only the labeled observations. Unlabeled observations are always beneficial to classification if the model we assume is correct. However, they may degrade the classifier performance when the model is misspecified. In the classical classification problem setting, many factors affect the semi-supervised performance, including training data, model specification, estimation method, and the classifier itself. For concreteness, we consider maximum likelihood estimation in finite mixture models and the Bayes plug-in classifier, due to their ubiquitousness and tractability. In this specific setting, we examine the effect of model misspecification on semi-supervised classification performance and shed some light on when and why performance degradation occurs.