In this work, we define and address Boundless Unsupervised Domain Adaptation (BUDA), a novel problem in semantic segmentation. BUDA set-up pictures a realistic scenario where unsupervised target domain not only exhibits a data distribution shift w.r.t. supervised source domain but also includes classes that are absent from the latter. Different to open-set and universal domain adaptation, which both regard never-seen objects as unknown, BUDA aims at explicit test-time prediction for these never-seen classes. To reach this goal, we propose a novel framework leveraging domain adaptation and zero-shot learning techniques to enable boundless adaptation on the target domain. Performance is further improved using self-training on target pseudo-labels. For validation, we consider different domain adaptation set-ups, namely synthetic-2-real, country-2-country and dataset-2-dataset. Our framework outperforms the baselines by significant margins, setting competitive standards on all benchmarks for the new task. Code and models are available at:~\url{this https URL}.