Programmable self-assembly of chained robotic systems holds potential for the automatic construction of complex robots from a minimal set of building blocks. However, current robotic platforms are limited to modules of uniform rigidity, which results in a limited range of obtainable morphologies and thus functionalities of the system. To address these challenges, we investigate in this paper the role of softness in a programmed self-assembling chain system. We rely on a model system consisting of “soft cells” as modules that can obtain different mechanical softness presettings. Starting from a linear chain configuration, the system self-folds into a target morphology based on the intercellular interactions. We systematically investigate the influence of mechanical softness of the individual cells on the self-assembly process. Also, we test the hypothesis that a mixed distribution of cells of different softness enhances the diversity of achievable morphologies at a given resolution compared to systems with modules of uniform rigidity. Finally, we illustrate the potential of our system by the programmable self-assembly of complex and curvilinear morphologies that state-of-the-art systems can only achieve by significantly increasing their number of modules.