The organelle involved in breaking down other organelles that have outlived their usefulness is the lysosome. Lysosomes are spherical organelles found in animal cells that contain a variety of hydrolytic enzymes. These enzymes are capable of breaking down a wide range of biological molecules, including proteins, carbohydrates, lipids, and nucleic acids.
Lysosomes are formed by the Golgi apparatus, which packages hydrolytic enzymes into vesicles and transports them to the lysosomes. When a lysosome fuses with another organelle, such as an old or damaged mitochondrion or peroxisome, the hydrolytic enzymes in the lysosome are released and begin to break down the organelle's molecules into smaller building blocks that can be recycled by the cell.
In this way, lysosomes play a critical role in the process of cellular degradation and recycling, helping to maintain the health and function of the cell by removing damaged or unnecessary organelles.