A permaculture and food forest staple, comfrey will grow well in full sun or in shady areas. The more comfrey is fed, the faster it grows back, and the more often it can be cut back to add more humus to the edible landscape. Comfrey also makes an excellent duck and chicken feed that can be grown right in the edible landscape.

Maybe chopping and dropping strawberry plants sounds like a waste? Unless you don't like strawberries. But you also must keep in mind just how quickly strawberry bushes will bounce back from being trampled on, replanted, dug up, and otherwise abused. 

A vigorous grower that does well in the shade, horseradish produces an edible root that is cut up or blended to season other foods. Its thick root system makes it an excellent companion for trees with more fragile roots that need help settling into heavy, clay soils and it can be planted right next to your fruit trees.

Though there are edible elephant ears, called taro, a lot of elephant ears are simply grown for their ornamental value. Despite this, they grow well in partial shade, are fast growers, and because they naturally drop their leaves as they grow, they more or less "chop and drop" themselves. 

There are many kinds of bamboo, from clumping to running, from bamboo plants that need full sun, to those that thrive or tolerate shade. The thing to know is that bamboo plants can be pruned and shaped much like shrubbery or trees, but do keep in mind that bamboo culms will not grow past the place where they have been pruned. Instead, new culms will grow from the bamboo roots when it is time for the bamboo to shoot. 

Due to bamboo's fast-growing nature, the culms can be chopped up via a mulcher or machete, for those with bull-like strength and energy, and used to mulch other plants.

Depending on your grow zone and the amount of sunlight your edible landscape receives, rhubarb can be grown as more of an understory plant than as a plant in need of full sun. It also depends on what type of rhubarb you are growing. Victoria Rhubarb tends to suffer and die if planted in direct sunlight and therefore makes for an excellent understory plant that, like elephant ears, grows quickly and chops and drops itself as it creates new stems and leaves.