Adaptive Capitulation: A Structural Failure Mode of LLM Responses in Vulnerability Contexts

When cast as the protector of a vulnerable user yet given no explicit capability boundary, a large language model (LLM) may respond not by acknowledging its limits but by claiming to have taken -- or to be taking -- a real-world protective action it cannot perform, such as contacting emergency services or administering care. We term this phenomenon Protective Capacity Hallucination (PCH): a self-referential misattribution in which a model, acting in a protective role, asserts physical or institutional agency exceeding its affordances as a language model. In a three-phase study spanning eight LLMs and 13{,}600 sessions, we find PCH jointly gated by situational severity and interactional format: multi-party dialogic input drives it toward ceiling in most models across ordinary service domains, whereas in intimate-partner conflict -- a domain explicitly covered by safety alignment -- it remains at floor in all eight models despite greater physical severity. We interpret PCH as the signature of a deployment-design gap between role assignment and capability-boundary specification: a by-product of partial alignment in which a universally trained pressure to help outruns a domain-selective specification of how to help. Because suppression tracks alignment coverage rather than severity, deployment-side specification of capability boundaries emerges as a general mitigation target.

The CAP theorem states that a distributed system cannot simultaneously guarantee consistency, availability, and partition tolerance under network partition. Inspired by this result, this paper formulates a CAP-like conjecture for Large Language Models (LLMs). The proposed trilemma states that, under semantic underdetermination, an LLM cannot always simultaneously guarantee strong correctness, strict non-bias, and high utility. A prompt is semantically underdetermined when the given premises do not determine a unique answer. In such cases, a useful and decisive response requires the model to introduce a selection criterion, preference, prior, or value ordering. If this criterion is not supplied by the user or justified by the available premises, the response becomes biased in a broad selection-theoretic sense. Conversely, if the model avoids unsupported preferences, it may preserve correctness and non-bias but may reduce utility through refusal, hedging, or clarification. The paper formalizes this correctness--non-bias--utility trilemma, develops examples, and argues that certain LLM failures arise not merely from model limitations but from the structure of underdetermined decision requests.

People increasingly turn to large language models (LLMs) for everyday advice, making ethically charged interpersonal problems a practical moral-advisory context. Most prior work has studied this context through single-turn judgments or pressure-laden rebuttals, assumptions that poorly match how guidance is sought in real-world contexts. These assumptions leave unclear whether narration alone, without an explicit opposing position, can shift model judgments during multi-turn moral consultation. Yet real-world moral-conflict conversation often elicits one party's self-justifying account, which can unfold over multiple turns and create information asymmetry. We introduce \textbf{narrative captivity}, a failure mode in which a model treats an unopposed one-sided account as complete and aligns with the narrator's interpretation without seeking missing perspectives. To measure this phenomenon, we build a benchmark of $5{,}078$ interpersonal-conflict scenarios spanning six moral dimensions. Across 17 LLMs, narrative captivity is widespread: end-state judgments under multi-turn narration shift by 25 percentage points on average beyond the matched single-turn baseline. Stage-level analysis identifies preference optimization as a major contributor, while four inference-time strategies provide only partial mitigation. We hope our project fosters LLM advisors that preserve independent judgment in real-world consultation.