The description of a space elevator falling is rendered in horrific detail in Kim Stanley Robinson’s Mars trilogy.
Twice.
Because the only known material strong enough at the time was diamond, and diamond doesn’t ablate much when falling through atmosphere.
One of the early space elevator research companies specifically designed a cable that was made by stacking successive layers of material both to slowly increase carrying capacity by building the tether in iterative layers, and hoping it would ablate or at least reach a quick terminal velocity in the case of catastrophic failure.
It is undoubtedly the case that the senior staff on that project were familiar with the Mars trilogy.
I've often wondered if we could decrease the difficulty of a space elevator by a good bit by integrating magnetic levitation.
The base would need to be enormous and I'm sure the power draw would be insane, but being able to break the elevator cable into smaller lines and take the weight off of any individual strand might make it a touch more plausible without currently non-existent technologies.
This was part of the Plot of Halo: ODST, where fragments of the space elevator collapsed onto New Mombasa.