Network slicing, a key component of post-5G networks, has brought virtual network embedding (VNE) to the forefront of networking research. However, existing VNE approaches are limited by their consideration of static network topologies, failing to account for the dynamic nature of real-world networks. This limitation becomes particularly problematic in the face of link failures or topology modifications, rendering these approaches ineffective. To address this, we propose a new service placement strategy that remains effective even when the network topology changes. Furthermore, we introduce several service migration strategies and thoroughly investigate their effectiveness. Our results demonstrate the adaptability of our proposed strategy, which leverages graph neural networks, in handling link failures without necessitating relearning. This adaptability underlines the potential of our approach to significantly enhance the robustness and flexibility of service migration in VNE, thereby contributing to the evolution of network slicing in post-5G networks.