The unfolding argument in the neuroscience of consciousness posits that causal structure cannot account for consciousness because any recurrent neural network (RNN) can be “unfolded” into a functionally equivalent feedforward neural network (FNN) with identical input-output behavior. Subsequent debate has focused on dynamical properties and philosophy of science critiques. We examine a boundary condition on the unfolding argument for RNN systems with rapid plasticity in their connection weights. We demonstrate through rigorous mathematical proofs that rapid plasticity negates the functional equivalence between RNN and FNN. Our proofs address history-dependent plasticity, dynamical systems analysis, information-theoretic considerations, perturbational stability, complexity growth, and resource limitations. We demonstrate that neuronal systems that possess properties such as plasticity, history-dependence, and complex temporal information encoding have features that cannot be captured by a static FNN. We show that plasticity is a concrete instance of lenient dependency between behavioral and internal observables, restoring empirical testability to theories that incorporate plasticity on perception-relevant timescales. Our results do not establish that recurrence, plasticity, or process are necessary for consciousness; they establish that the unfolding argument does not preclude empirical investigation of whether these properties matter.