The right to be forgotten requires the removal or "unlearning" of a user's data from machine learning models. However, in the context of Machine Learning as a Service (MLaaS), retraining a model from scratch to fulfill the unlearning request is impractical due to the lack of training data on the service provider's side (the server). Furthermore, approximate unlearning further embraces a complex trade-off between utility (model performance) and privacy (unlearning performance). In this paper, we try to explore the potential threats posed by unlearning services in MLaaS, specifically over-unlearning, where more information is unlearned than expected. We propose two strategies that leverage over-unlearning to measure the impact on the trade-off balancing, under black-box access settings, in which the existing machine unlearning attacks are not applicable. The effectiveness of these strategies is evaluated through extensive experiments on benchmark datasets, across various model architectures and representative unlearning approaches. Results indicate significant potential for both strategies to undermine model efficacy in unlearning scenarios. This study uncovers an underexplored gap between unlearning and contemporary MLaaS, highlighting the need for careful considerations in balancing data unlearning, model utility, and security.