Pruning is a process designed to reduce the number of weights in a large neural network. This can substantially speed up inference but might cause a considerable reduction in the model's accuracy, and thus it is usually followed by a healing process that regains some of the lost accuracy. In this paper, we propose a new healing method, STARFISH, that can recover (most of) the accuracy of any pruned network efficiently. The main idea of STARFISH is to optimize the pruned network to align with the original network's internal state representations using a tiny calibration set of unlabeled examples. For the common case of removing 50% of the weights, STARFISH healing improves the recovered accuracy by up to 22% over the state-of-the-art methods on ViT-based networks. Its advantage is even more pronounced under aggressive pruning. For example, after eliminating 75% of the weights in a DeiT-B network for ImageNet, STARFISH uses only 0.4% of the number of training images as a calibration set and recovers 82% of the original dense accuracy, whereas competing recovery techniques reach only 40% of the dense model accuracy.