Traditional machine learning assumes a stationary data distribution, yet many real-world applications operate on nonstationary streams in which the underlying concept evolves over time. This problem can also be viewed as task-free continual learning under concept drift, where a model must adapt sequentially without explicit task identities or task boundaries. In such settings, effective learning requires both rapid adaptation to new data and forgetting of outdated information. A common solution is based on a sliding window, but this approach is often computationally demanding because the model must be repeatedly retrained from scratch on the most recent data. We propose a different perspective based on machine unlearning. Instead of rebuilding the model each time the active window changes, we remove the influence of outdated samples using unlearning and then update the model with newly observed data. This enables efficient, targeted forgetting while preserving adaptation to evolving distributions. To the best of our knowledge, this is the first work to connect machine unlearning with concept drift mitigation for task-free continual learning. Empirical results on image stream classification across multiple drift scenarios demonstrate that the proposed approach offers a competitive and computationally efficient alternative to standard sliding-window retraining. Our implementation can be found at \hrehttps://anonymous.4open.science/r/MUNDataStream-60F3}{https://anonymous.4open.science/r/MUNDataStream-60F3}.