The self-assembly of particles into organized structures is a key feature of living organisms and a major engineering challenge. While it may proceed through the binding of perfectly matched, puzzle-piece-like particles, many other instances involve ill-fitting particles that must deform to fit together. These include some pathological proteins, which have a known propensity to form fibrous aggregates. Despite this observation, the general relationship between the individual characteristics of the particles and the overall structure of the aggregate is not understood. To elucidate it, we analytically and numerically study the selfassembly of two-dimensional, deformable ill-fitting particles. We find that moderately sticky particles tend to form equilibrium self-limited aggregates whose size is set by an elastic boundary layer associated with collective deformations that may extend over many particles. Particles with a soft internal deformation mode thus give rise to large aggregates. In addition, when the particles are incompressible, their aggregates tend to be anisotropic and fiberlike. Our results are preserved in a more complex particle model with randomly chosen elastic properties. This indicates that generic proteinlike characteristics such as allostery and incompressibility could favor the formation of fibers in protein aggregation, and suggests design principles for artificial self-assembling structures.