The elimination of old and worn out cells is done by a cell organelle called lysosomes. It is also called the waste disposal system of a cell.
This lysosomes has powerful digestive enzymes that break down all organic organelles.
When a cell is about to be destroyed, this lysosomes burst and the digestive enzymes will spread everywhere in the cells. So, the cell becomes completely destroyed. So, the lysosomes are also called the suicidal bags of a cell.