Final answer:
The phase where the nuclear envelope breaks down and chromosomes are released into the cytoplasm is prometaphase, following prophase and preceding metaphase in the cell cycle.
Step-by-step explanation:
The phase where the nuclear envelope is broken open and the chromosomes are released into the cytoplasm is known as prometaphase. During this phase, the nuclear envelopes are completely broken down, allowing the spindle to interact with the chromosomes. Each sister chromatid forms an individual kinetochore that attaches to microtubules from opposite poles. This stage follows prophase, during which the nuclear envelope starts to dissociate, and precedes metaphase, where chromosomes line up at the cell center.