Final answer:
The cells showing swollen, ragged nuclei, and poorly stained features are undergoing karyolysis, which is the dissolution of a cell's nucleus typically as a result of necrosis.
Step-by-step explanation:
The description of cells on the cytology slide showing signs of swollen, ragged nuclei with non-intact nuclear membranes and poor staining suggests the cells are undergoing karyolysis. Karyolysis is the process where the cell nucleus is breaking down, often due to necrosis—where cells die from external injury rather than a programmed death like apoptosis. The nuclear membrane dissolves and the chromatin of the nucleus fades due to the activity of DNAases and RNAses during this process. This is distinct from pyknosis and karyorrhexis, which are other forms of nuclear change often associated with apoptosis, where the nucleus shrinks and fragments, respectively, and unlike phagocytosis, which is the process of a cell engulfing particles or other cells.