Elevated voltages (above normal) on a weak cable can cause cable failure at one of those weak points. AC high voltage testing at elevated voltages (at 50/60Hz or VLF testing) can cause weak elements in a cable to fail. It has nothing to do with the frequency of the applied voltage waveform and everything to do with the pressure - that is the voltage, applied.
As long as one follows the correct standards for withstand testing and the cable fails this test, then depending on your interpretation of word "destructive", you have exposed and detected a severe weakness in the cable, that would very likely have failed in normal service. The big difference is that a failure under test has very limited current and therefore power injected into the fault, while a unplanned failure under service, can cause catastrophic and collateral damage to other devices in the area of the failure and customer interruptions etc.
Note that based on extensive research performed by a large university, they found that about 3% of cables may fail a withstand test if one applies the correct withstand voltages, so don't think that every cable you perform a withstand test will fail. Only those that have very severe defects will run to failure.
Also, learn more about VLF and Hipot testing here.
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