No direct reference to JCP, but there are a number of stores that have made a successful transition from brick and mortar to internet sales. Some have a good history of mail order sales as well.
Two entities that come to mind are large camera/electronics outlets located in New York. The local camera store is gone in all but the largest markets. And yet, these stores remain in brick and mortar as well as having huge online sales.
They are the ones to study if you want to remain in business. Companies like Sears needs to do more of this, if it’s not too late for them.