Spontaneous scalarization provides a dynamical mechanism to evade the no-hair paradigm, but it has been argued to generically eliminate the Cauchy horizon in charged black holes. We show that this obstruction is not universal, but instead follows from the sign-definite structure of the Einstein-Maxwell source term. Within the $P$-dual formulation of nonlinear electrodynamics, we derive a general condition under which the effective scalar source changes sign between the horizons, allowing the integral constraint to be satisfied without destroying the Cauchy horizon. This establishes that the fate of the Cauchy horizon depends on the electromagnetic coupling and identifies candidate theories where scalarized horizons may persist. The resulting framework opens the possibility of studying scalarization in the interhorizon region and its interplay with mass inflation.

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• Alternative gravity theories
• Classical black holes