Face Image Quality Assessment (FIQA) evaluates the utility of a face image for automated face recognition (FR) systems. In this work, we propose PreFIQs, an unsupervised and training-free FIQA framework grounded in the Pruning Identified Exemplar (PIE) hypothesis. We hypothesize that low-utility face images rely disproportionately on fragile network parameters, resulting in larger geometric displacement of their embeddings under model sparsification. Accordingly, PreFIQs quantifies image utility as the Euclidean distance between L2-normalized embeddings extracted from a pre-trained FR model and its pruned counterpart. We provide a first-order theoretical justification via a Jacobian-vector product analysis, demonstrating that this empirical drift serves as a computationally efficient approximation of the exact geometric sensitivity of the latent embedding manifold. Extensive experiments across eight benchmarks and four FR models demonstrate that PreFIQs achieves competitive or superior performance compared to state-of-the-art FIQA methods, including establishing new state-of-the-art results on several benchmarks, without any training or supervision. These results validate parameter sparsification as a principled and practically efficient signal for face image utility, and demonstrate that quality is, in essence, what survives pruning.