The dieback appears to be caused, at least in part, by Volutella Blight, a fairly common fungal disease that affects both Pachysandra and its relative Boxwood. It might be overlapping with scorch from drought stress, depending on whether the planting has been regularly irrigated. The linked page has information about management, which essentially just involves mowing-down all Pachysandra growth, raking it up and disposing of it, and letting the patch regrow at its own pace. If the planting has healthy roots, it should rebound well, though monitor it for watering needs so it has enough moisture to regrow. (Feel the soil around five inches deep and water thoroughly once it becomes somewhat dry to the touch at that depth.)

If either planting is in full sun (or mostly sun), that will exacerbate plant stress and raise the risk of scorch, since Pachysandra does best under trees and in locations with some degree of shade during the hotter afternoon hours. (The lilac growing with them in the circle look like they're in full sun, as lilacs would want, which is why we're mentioning it.)

Miri