The invalid state root can end up at the light client if any full node that it’s connected to feeds it the invalid block, because light clients just assume that the chain with the most work is valid. Under normal circumstances this should not happen, but in the rare case that the majority of the consensus is malicious then this can happen. Or even if people decided to fork the chain for sincere reasons e.g. due to disagreements, then light clients wouldn’t be able to distinguish between the forks if the consensus algorithms are the same.
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