Borderless and partially ruled scientific tables often omit visual boundaries that mark logical rows, columns, and spanning regions. We introduce Tabstructor, a vision–language framework for latent-border reconstruction: predicting a table bounding box and horizontal and vertical segments representing logical boundaries even when visually absent or incomplete. On a held-out external test set, we compare task-specific prompting of a frozen base model, supervised fine-tuning, structure-preserving augmentation, and optional OCR-assisted geometry refinement. We introduce the Latent Border Reconstruction Score (LBRS; 0–100, higher is better) for evaluating valid structural and geometric border recovery. Task-specific prompting improves the frozen model, while fine-tuning provides the dominant gain, increasing LBRS from 38.552 to 90.014 (paired gain 51.462; 95% paired-bootstrap CI: 45.583–57.259). The augmented predictor reaches 93.487, a further 3.473-point gain, although it receives additional cumulative training exposure. OCR-assisted refinement improves boundary localisation and extent but adds only 0.467 points on average (95% CI: -1.968–2.615) and can cause boundary-count regressions. Thus, fine-tuning performs the principal reconstruction, while refinement is an optional, non-uniform geometry adjustment.