Transformer circuits are often evaluated by ablating certain circuits or components and measuring the resulting performance drop. These interventions test circuit necessity only under a fixed model configuration, and it is unclear if the residual network can recover performance through alternative, parameter-efficient adaptations. Using BERT as a frozen encoder and a linear part-of-speech (POS) readout as a task classifier, we first use gate masking to learn a sparse core subnetwork sufficient for POS classification. Ablating this core produced a damaged model and a sharp drop in accuracy (95.0\\% \\rightarrow 16.8\\%)$. We then evaluated recovery from damage under four retraining pathways: readout-only, mask-only, joint readout+mask, and encoder-only with the ablation held fixed. Readout-only, mask-only, joint mask-and-readout, and encoder-only retraining arrived at 80.0\%, 69.7\%, 85.9\%, and 92.3\% accuracy, respectively. Some recovery pathways partially restored core-like geometry, but others recovered high performance without restoring the original encoder geometry. These results show that in a joint encoder--readout context, a sparse subnetwork can be sufficient and necessary for performance in the original fixed configuration, but need not remain necessary after recovery, and that recovered performance does not rely on recovering the original geometry.