While in-context learning is generally shown to be effective for Large Language Models (LLMs), misleading or flawed contexts can cause performance degradation and mode collapse, an empirical phenomenon we term "pigeonholing". Unintentionally bad contexts can happen without jailbreak intent. For example, a user prompts the model to justify an incorrect math theorem or fails to correct buggy agent code. Specifically, we investigate pigeonholing in two settings: (1) when a user suggests an incorrect solution, and (2) when the multi-turn dialogue history contains the assistant’s incorrect answers from prior turns. Our evaluations across 10 verifiable and open-ended tasks with 10 different models show that pigeonholing manifests in three distinct ways: (1) repeating the incorrect answers from the context (causing a 38-40% performance drop), (2) reducing answer diversity in open-ended text generation, and (3) reversing stances on controversial topics to align with the previous user or assistant’s perspective. Further, we find that pigeonholing worsens almost monotonically with context length (i.e., conversation turns). Finally, while standard RLVR-trained models show improvements on clean prompts, they fail to maintain performance on corrupted contexts. We take a step towards mitigating model vulnerability by training with RLVR on synthetic errors, improving model performance on bad contexts by 43–60% over vanilla baselines.