What is the term that refers to the breaking down of dead organisms and wastes done by prokaryotes?

The answer is decomposers.

After the death of producers and consumers, decomposers (such as Actinobacteria, or other bacteria which are prokaryotes) eat that dead organisms and carbon, nitrogen, and other elements are released into the environment. It should be taken into consideration that eukaryotes (such as fungi) can be decomposers as well.