That's not to say that cables or ropes cannot fail, but when they do so, failure of many individual components is required.
A recent example is the failure of support cables for the Arecibo radio observatory in Puerto Rico in 2020. This was the result of a progressive failure played out over months, though at an accelerating rate, until the final catastrophic failure and loss of the instrument as a whole. (This wasn't wholly unforseen and was precipitated by a long period of rather intentional neglect of maintenance.)
Even after the failure of two complete cables, the remaining cables supported the load of Arecibo's instrument platform. On 1 December 2020, strands of one of the remaining cables began breaking, at an accelerating rate, leading to the total failure of that cable, then a second and third, and with it loss of the instrument platform. The final moments were captured on video.
Sequence begins at about 55s here: https://yewtu.be/watch?v=b3AASKr_iHc