I assume that the plumb tree is grafted. If the live growth is above the graft then there is hope to save the tree. On damaged trees, I cut all dead and rotten material back until the cut has only clean wood. After pruning, let the plant shoot out new growth, and gradually prune to select main branches to give the tree the desired shape. You may want to google the proper shape for plum trees, to help guide your selection of central leader and placement of retained branches.
Eclectic gardening style, drawing from 45 years of interest and experience. Mostly plant in raised beds and containers primarily using intensive gardening techniques.