Competing interactions produce finite-size textures in myriad condensed matter systems, typically forming elongated stripe or round bubble domains. Transitions between stripe and bubble phases, driven by field or temperature, are expected to be reversible in nature. Here we report on the distinct character of the analogous transition for nanoscale spin textures in chiral Co/Pt-based multilayer films, known to host N{e}el skyrmions, using microscopy, magnetometry, and micromagnetic simulations. Upon increasing field, individual stripes fission into multiple skyrmions, and this transition exhibits a macroscopic signature of irreversibility. Crucially, upon field reversal, the skyrmions do not fuse back into stripes, with many skyrmions retaining their morphology down to zero field. Both the macroscopic irreversibility and the microscopic zero-field skyrmion density are governed by the thermodynamic material parameter determining chiral domain stability. These results establish the thermodynamic and microscopic framework underlying ambient skyrmion generation and stability in chiral multilayer films and provide immediate directions for their functionalization in devices.