As machine learning models become increasingly complex, concerns about their robustness and trustworthiness have become more pressing. A critical vulnerability of these models is data poisoning attacks, where adversaries deliberately alter training data to degrade model performance. One particularly stealthy form of these attacks is subpopulation poisoning, which targets distinct subgroups within a dataset while leaving overall performance largely intact. The ability of these attacks to generalize within subpopulations poses a significant risk in real-world settings, as they can be exploited to harm marginalized or underrepresented groups within the dataset. In this work, we investigate how model complexity influences susceptibility to subpopulation poisoning attacks. We introduce a theoretical framework that explains how overparameterized models, due to their large capacity, can inadvertently memorize and misclassify targeted subpopulations. To validate our theory, we conduct extensive experiments on large-scale image and text datasets using popular model architectures. Our results show a clear trend: models with more parameters are significantly more vulnerable to subpopulation poisoning. Moreover, we find that attacks on smaller, human-interpretable subgroups often go undetected by these models. These results highlight the need to develop defenses that specifically address subpopulation vulnerabilities.