Plum trees are susceptible to a number of fungal infections. I can see signs on your daughter's tree which might be silverleaf and/or brown rot - but there could be others too.
Fungal infections get in through a wound in the tree...but this can be as simple as the damage caused by a bird pecking at the fruit.
If it were my tree I would take all the fruit off and prune out the worst diseased branches. The time to prune is in summer for a plum tree. Remove all the removed parts from the site or burn them. The removal is important as rotten wood and/or fruit sitting around will enable the fungus to pass back to the tree. Fruit rotting around the tree in autumn is a route to reinfection.
Then I'd look after the tree like fury. If it's in a lawn, remove the grass from the area around it, weed around the tree (to remove competition),and apply a thick mulch of compost and bark. Water thoroughly and often. Then wait and see what happens next year. In a year or two things might improve. If not repeat all the above. If things don't improve then you would have tried your best and it might be time to remove the tree.
I'm a gardener not a tree expert, so if someone comes along with better knowledge I'll be all ears.