Relationships are essential to our happiness and wellbeing. The dissolution of a relationship, the final stage of relationship's lifecycle and one of the most stressful events in an individual's life, can have profound and long-lasting impacts on people. With the breakup process increasingly facilitated by computer-mediated communication (CMC), and the likely future influence of AI-mediated communication (AIMC) tools, we conducted a semi-structured interview study with 21 participants. We aim to understand: 1) the current role of technology in the breakup process, 2) the needs and support individuals have during the process, and 3) how AI might address these needs. Our research shows that people have distinct needs at various stages of ending a relationship. Presently, technology is used for information gathering and community support, acting as a catalyst for breakups, enabling ghosting and blocking, and facilitating communication. Participants anticipate that AI could aid in sense-making of their relationship leading up to the breakup, act as a mediator, assist in crafting appropriate wording, tones, and language during breakup conversations, and support companionship, reflection, recovery, and growth after a breakup. Our findings also demonstrate an overlap between the breakup process and the Transtheoretical Model (TTM) of behavior change. Through the lens of TTM, we explore the potential support and affordances AI could offer in breakups, including its benefits and the necessary precautions regarding AI's role in this sensitive process.