Several efforts have been made to synthesize semi-supervised learning (SSL) and open set recognition (OSR) within a single training policy. However, each attempt violated the definition of an open set by incorporating novel categories within the unlabeled training set. Although such \textit{observed} novel categories are undoubtedly prevalent in application-grade datasets, they should not be conflated with the OSR-defined \textit{unobserved} novel categories, which only emerge during testing. This study proposes a new learning policy wherein classifiers generalize between observed and unobserved novel categories. Specifically, our open-set learning with augmented category by exploiting unlabeled data (Open-LACU) policy defines a background category for observed novel categories and an unknown category for unobserved novel categories. By separating these novel category types, Open-LACU promotes cost-efficient training by eliminating the need to label every category and ensures safe classification by completely separating unobserved novel categories that appear over time. Finally, we present a unified approach to establish benchmark results for this emerging and more application-grade learning policy.