Under the averaged weak energy condition (AWEC), Cauchy horizons are inherently unstable.
However, cases of AWEC violation, such as the Casimir effect caused by periodic boundary conditions, do exist, and since the region of spacetime inside the Cauchy horizon has closed timelike curves it is subject to periodic boundary conditions.
If the spacetime inside the Cauchy horizon violates AWEC, then the horizon becomes stable and frequency boosting effects would be canceled out by the tendency of the spacetime to act as a divergent lens.
In 2018, it was shown that the spacetime behind the Cauchy horizon of a charged, rotating black hole exists, but is not smooth, so the strong cosmic censorship conjecture is false.
In the 2020 film Palm Springs, the character Sarah mentions the Cauchy horizon as she formulates a plan to escape a time loop.