Polycapillary x-ray focusing devices are built from hundreds of thousands of bent microcapillaries that are stacked into hexagonal arrays. We show that intrinsic point defects of the optics (e.g., missing or larger capillaries) lead to the formation of multiple x-ray images of an object positioned in the focal plane. These images can be recorded in parallel, and can provide spatial resolution that is limited by the defect size and not by the focal spot size. In a proof-of-principle experiment, we demonstrate submicron resolution, which has not yet been achieved with polycapillary focusing optics. Tailored optics with a controlled distribution of "defects" could be used for multimodal nanoscale x-ray imaging with laboratory setups.