<p>Self-folding materials capable of autonomous transitions between two- and three-dimensional states are widespread in biological active solids and are relevant to engineered systems. However, the programmability and robustness of self-folding behaviour, particularly in living tissues, remain poorly understood. Here we study a self-folding and unfolding mode in the early-diverging aneural animal <i>Trichoplax adhaerens</i>. We discover sharp crease lines that act as one-dimensional domain walls, compartmentalizing the animal’s cilia orientation field into disjointed patches. These creases undergo rapid geometric and topological remodelling on a timescale of seconds, driven by the interplay of tissue buckling, surface adhesion and ciliary activity. Elementary unit operations such as merging and splitting organize the creases into a dynamic defect network at the interface between the animal’s ciliated epithelium and its substrate. We show that creases locally disrupt ciliary coordination, act as information bottlenecks between adjacent ciliary patches and establish a feedback loop between ciliary activity and crease geometry. This feedback confers self-limiting behaviour, enabling the emergence of anticorrelated active states that remove the crease. This emergent mechanism suggests design principles for a class of robust, self-folding two-dimensional materials and demonstrates how information bottlenecks can manifest physically as creases in soft epithelial tissue.</p>