Approximately 90 participants diagnosed with persistent corneal epithelial defect (PCED) will be enrolled at multiple US centers in a study to assess the safety and efficacy of KPI-012, a topical mesenchymal stem cell secretome therapy. After an initial cohort of at least 2 participants to evaluate the safety of the high strength product, participants in the second cohort will be randomized to treatment with either the product or vehicle (placebo) for 8 weeks. The percentage of healing will be compared between groups treated with product and vehicle. Total length of study participation will be approximately 34 weeks.