Final answer:
The organism that digests tissues of dead animals and lacks a nucleus is a type of bacteria, which are prokaryotes and serve as decomposers in the ecosystem.
Step-by-step explanation:
The single-celled organism that causes dead animals to really stink while digesting their tissues, and which lacks a nucleus in its cell, is a type of bacteria. Bacteria are classified within the kingdom Prokaryotae (also called Monera), which includes all prokaryotes. These organisms are known for their role as decomposers and are integral to the ecosystem because they break down dead organic material, such as the remains of a predator's kill, contributing to the nutrient cycle. Unlike eukaryotes, prokaryotes do not have a nucleus or other membrane-bound organelles within their cells.
Specifically, the bacteria that cause putrefaction in dead animals are known as saprotrophic bacteria. These bacteria are a type of scavenger decomposer and are different from fungi, which are also decomposers but belong to a different kingdom altogether.