The liver of a dog has been found to have higher than normal cell death because the dna is damaged. What part of the cell failed to do its job of protecting the dna of the cell

This is a slightly vague question because there are many reasons why DNA can be damaged and determining which organelle was at fault is generally a case by case matter. but the only part of a cell that you could considered to be tasked with protecting genetic material is the nuclear envelope which is simply a phospholipid bilayer surrounding the nucleus and/or the nucleolus so I would say the answer is the nuclear membrane and/or nuclear envelope.