Most fruit trees sucker frequently. In addition, research reveals that fruit trees under stress are more inclined to shoot suckers than healthy ones. Over pruning of trees also stimulates sucker growth. Many fruit trees are grafted to a root stock, which provides hardiness and growth regulation, but is not the tree you selected for the fruit production. These suckers may or may not be an edible stone fruit (sometimes they use other Prunus).

Plant two different, compatible varieties of plums to ensure fruit. Cherries are self- fruitful.

I have had some suckers on both plums and cherries.

https://extension.umn.edu/fruit/growing-stone-fruits-home-garden