Pretrained vision-language-action (VLA) policies provide strong language-conditioned manipulation knowledge, but they remain largely vision-driven and can struggle once manipulation enters contact states where the scene is occluded, depth is ambiguous, or small force errors push execution off the offline demonstration distribution. We present LIFT (Late Reactive Injection of Force for VLA Post-Training), a force-aware post-training framework that adds contact reactivity to a pretrained VLA policy while preserving its output at initialization. LIFT grafts a reactive action expert beside the original action expert, initializes it from pretrained action weights, and injects recent 6D end-effector force through causal force memory and zero-initialized cross attention, enabling actions to be refreshed during execution. To address the policy-dependent distribution shift of contact feedback, LIFT further couples reactive force injection with an online DAgger loop that trains on a mixture of offline task-alignment data and human-corrected online rollouts. Across towel folding, book insertion, and Hanoi ring placement, LIFT learns faster and reaches higher peak and final performance than vision-only DAgger, while ablations show that reactive force memory and online corrective data are both important for robust contact-rich manipulation. Our code is publicly available at https://github.com/y-wng/lift

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