The primary characteristic of a decomposer in an ecosystem is its ability to break down organic matter from dead plants and animals. Decomposers, including bacteria and fungi, play a crucial role in the nutrient cycle by recycling nutrients back into the soil, which supports producers like plants. This process not only enriches the soil but also helps maintain the ecological balance by preventing the accumulation of waste, thus ensuring a sustainable ecosystem. Without decomposers, ecosystems would be overwhelmed with organic waste, disrupting the flow of energy and nutrients.