Final answer:
The phase of the cell cycle with chromatin condensation and the breakdown of the nuclear envelope is prophase, the first stage of mitosis. Telophase is the stage where chromosomes decondense and new nuclear envelopes form.
Step-by-step explanation:
The phase of the cell cycle characterized by chromatin condensation and the breakdown of the nuclear envelope is known as prophase. During prophase, the loosely packed chromatin coils and condenses into visible chromosomes, and the nuclear membrane starts to disintegrate. It's the first stage of mitosis where the nucleolus also disappears and the centrosomes begin to move to opposite poles, facilitating the formation of the mitotic spindle.
In contrast, the unpacking of chromosomes and the formation of a new nuclear envelope characterizes telophase. During this stage, chromosomes begin to decondense, transforming back into chromatin, and new nuclear membranes start to form around each set of chromosomes at the opposite poles of the cell, marking the final stage of mitosis before cytokinesis.