Conversational AI is increasingly deployed in emotionally charged and ethically sensitive interactions. Previous research has primarily concentrated on emotional benchmarks or static safety checks, overlooking how alignment unfolds in evolving conversation. We explore the research question: what breakdowns arise when conversational agents confront emotionally and ethically sensitive behaviors, and how do these affect dialogue quality? To stress-test chatbot performance, we develop a persona-conditioned user simulator capable of engaging in multi-turn dialogue with psychological personas and staged emotional pacing. Our analysis reveals that mainstream models exhibit recurrent breakdowns that intensify as emotional trajectories escalate. We identify several common failure patterns, including affective misalignments, ethical guidance failures, and cross-dimensional trade-offs where empathy supersedes or undermines responsibility. We organize these patterns into a taxonomy and discuss the design implications, highlighting the necessity to maintain ethical coherence and affective sensitivity throughout dynamic interactions. The study offers the HCI community a new perspective on the diagnosis and improvement of conversational AI in value-sensitive and emotionally charged contexts.