Hi Matt,

Thank you for submitting your question to the UVM Master Gardener Helpline and thanks so much for the photos. They were very helpful and are consistent with "brown rot". Brown rot is a fungal disease of stone fruits such as plums. This overwinters in affected twigs, branches and shriveled fruits. 

Pruning of affected twigs and branches, and cleaning up and disposing of all infected fruit is key to control. The severity of brown rot is dependent on the weather. Summers with frequent rainfall, like last summer, and high humidity lead to the greatest disease incidence.

Luckily, brown rot is not a lethal disease. However, once fruits are infected, there are no curative treatments. To manage twig infections, prune four to six inches below sunken or dead tissue on each branch. Dispose of these branches by burning or burying them. To prevent spread of brown rot fungi on pruning tools, decontaminate tools between each cut by dipping them for at least 30 seconds in 70% alcohol.

To reduce the chance of infection in subsequent years, remove all fruit from the tree and from the ground and prune out infected twigs after harvest. Burn, bury, or otherwise remove these infections from the orchard. This practice will reduce the number of spores present the following season. Prune the trees to maintain good air circulation which will promote rapid drying.

There are several good references on the cause and treatment of this disease. I particularly like the article from University of Minnesota extension:

https://extension.umn.edu/plant-diseases/brown-rot-stone-fruit

https://ohioline.osu.edu/factsheet/plpath-fru-29

You may find that your trees do not look as severely affected as those in these articles, likely because European plums are more susceptible than Japanese plums. Best of luck with revival of your trees.