Final answer:
A phage DNA remains a prophage within a bacterial cell as long as certain phage genes are repressed, which keeps it in an inactive lysogenic cycle until stressful conditions trigger its transition to the lytic cycle.
Step-by-step explanation:
The phage DNA can remain in the prophage state in a bacteria as long as certain phage genes are repressed. This condition is representative of the lysogenic cycle, where the phage DNA is integrated into the bacterial genome and can stay dormant for many generations as long as it remains inactive. This inactive state is maintained primarily by repressor proteins that prevent the transcription of phage genes that could initiate the lytic cycle. Stressful conditions, however, such as starvation or exposure to toxic chemicals, may lead to the induction process, where the repressor is removed, allowing the phage DNA to excise from the bacterial chromosome and enter the lytic cycle, thereby terminating the prophage state.