This work delves into the complexities of machine unlearning in the face of distributional shifts, particularly focusing on the challenges posed by non-uniform feature and label removal. With the advent of regulations like the GDPR emphasizing data privacy and the right to be forgotten, machine learning models face the daunting task of unlearning sensitive information without compromising their integrity or performance. Our research introduces a novel approach that leverages influence functions and principles of distributional independence to address these challenges. By proposing a comprehensive framework for machine unlearning, we aim to ensure privacy protection while maintaining model performance and adaptability across varying distributions. Our method not only facilitates efficient data removal but also dynamically adjusts the model to preserve its generalization capabilities. Through extensive experimentation, we demonstrate the efficacy of our approach in scenarios characterized by significant distributional shifts, making substantial contributions to the field of machine unlearning. This research paves the way for developing more resilient and adaptable unlearning techniques, ensuring models remain robust and accurate in the dynamic landscape of data privacy and machine learning.