Cold drawing, a well-established processing technique in the polymer industry, was recently revisited and discovered as an efficient material structuring method to create ordered patterns in composites consisting of both cold-drawable polymers and brittle target materials. Such a high-yield and low-cost manufacturing technique enables the large-scale fabrication of micro-ribbon structures for a wide range of functional materials, including two-dimensional (2D) layered materials. Compared to the abundant phenomenological results from experiments, however, the underlying mechanisms of this technique are not fully explored. Here, supported by experimental investigation, finite element calculations, and theoretical modeling, we systematically study the effect of a capping layer on the controlled fragmentation of 2D materials deposited on polymer substrates during the cold drawing. The capping layer is found to prevent the premature fracture of the 2D thin films during elastic deformation of the substrate, when a specific requirement proposed by the theoretical model is satisfied. Controlled fragmentation is enabled in the necking stage due to the protective effect of the capping layer, which also influences the size of the resulting fragments. Flexible and stretchable electrodes based on 2D material ribbons are fabricated to demonstrate the effectiveness of the proposed roadmap. This study gives an accurate understanding of interactions between 2D materials, polymer substrates, and capping layers during cold drawing, and offers guidance for potential applications such as flexible electronics.