Self-adaptive systems continuously adapt to changes in their execution environment. Capturing all possible changes to define suitable behaviour beforehand is unfeasible, or even impossible in the case of unknown changes, hence human intervention may be required. We argue that adapting to unknown situations is the ultimate challenge for self-adaptive systems. Learning-based approaches are used to learn the suitable behaviour to exhibit in the case of unknown situations, to minimize or fully remove human intervention. While such approaches can, to a certain extent, generalize existing adaptations to new situations, there is a number of breakthroughs that need to be achieved before systems can adapt to general unknown and unforeseen situations. We posit the research directions that need to be explored to achieve unanticipated adaptation from the perspective of learning-based self-adaptive systems. At minimum, systems need to define internal representations of previously unseen situations on-the-fly, extrapolate the relationship to the previously encountered situations to evolve existing adaptations, and reason about the feasibility of achieving their intrinsic goals in the new set of conditions. We close discussing whether, even when we can, we should indeed build systems that define their own behaviour and adapt their goals, without involving a human supervisor.