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Traditional program slicing techniques are crucial for early bug detection and manual/automated debugging of online code snippets. Nevertheless, their inability to handle incomplete code hinders their real-world applicability in such scenarios. To overcome these challenges, we present NS-Slicer, a novel learning-based approach that predicts static program slices for both complete and partial code. Our tool leverages a pre-trained language model to exploit its understanding of fine-grained variable-statement dependencies within source code. With this knowledge, given a variable at a specific location and a statement in a code snippet, NS-Slicer determines whether the statement belongs to the backward slice or forward slice, respectively. We conducted a series of experiments to evaluate NS-Slicer’s performance. On complete code, it predicts the backward and forward slices with an F1-score of 97.41% and 95.82%, respectively, while achieving an overall F1-score of 96.77%. Notably, in 85.20% of the cases, the static program slices predicted by NS-Slicer exactly match entire slices from the oracle. For partial programs, it achieved an F1-score of 96.77%–97.49% for backward slicing, 92.14%–95.40% for forward slicing, and an overall F1-score of 94.66%–96.62%. Furthermore, we demonstrate NS-Slicer’s utility in vulnerability detection (VD), integrating its predicted slices into an automated VD tool. In this setup, the tool detected vulnerabilities in Java code with a high F1-score of 73.38%. We also include the analyses studying NS-Slicer’s promising performance and limitations, providing insights into its understanding of intrinsic code properties such as variable aliasing, leading to better slicing.