The material you are describing is probably a marble known as rossa perlinio. This type of marble, when it is formed has mud running through it and this is what the soft veins are---mud. Unfortunately the only cure is to fill the veins as the erode out.
TIP These veins can be filled with polyester or if you have a lot of veining you can use a colored unsanded grout.
Article ID: 467
Created: January 20, 2022
Last Updated: January 20, 2022
Author: Pam Freitag
Online URL: https://sr-manual.com/kb/article/we-have-a-pink-marble-tile-that-has-some-brown-veins-and-the-veins-are-soft-and-coming-out-is-there-anything-we-can-do-to-stop-these-veins-from-softening-467.html