Persistent corneal epithelial defect (PCED) is a persistent non-healing corneal defect or wound. KPI-012 is a novel, human bone-marrow derived human mesenchymal stem cell (hMSC) secretome composed of biologically active components, which have been shown in preclinical studies and early clinical trials to facilitate corneal healing. This study will investigate the efficacy and safety of KPI-012 eye drops 4 times daily for 8-weeks for healing of PCED.