This study is a randomized, multicenter, double-masked, vehicle-controlled study to evaluate the safety and efficacy of NEXAGON (lufepirsen ophthalmic gel) in subjects with persistent corneal epithelial defects (PCED). The study will enroll subjects who will complete a Screening Period, Treatment Period (up to 8 weeks) and Follow-up Period (4 weeks). Those subjects whose defect has not re-epithelialized by the completion of the Treatment Period or who achieved re-epithelialization but failed to maintain re-epithelialization for 28 days after treatment completion (durability) are eligible to enter the NEXAGON Open-label Treatment Period for an additional 8 weeks.