Saprophages (from the Greek word sapros: putrid and phàgos: eater) feed on decomposing matter.
The term saprophyte is also used, although incorrectly as it refers to a saprophage plant, and saprophage plants do not exist (the term was used when fungi were considered to be plants). The word saprophyte is more often used more often when there is no ingestion and the decomposing matter is absorbed through a membrane.
If the decomposing matter is a rotting carcass, then the term necrophagy is preferred.
Worms are saprophage organisms. © Sparrows friend, Flickr, CC by nc-nd 2.0