I don't know how dying the fabric would break down the material. All that dye is color that "stains" the fabric. Think of spilling coffee or something else on a shirt or other piece of clothing. If it isn't treated fairly soon, it stains the fabric, yet the fabric is still good.
To get the dye to take in nylon you have to use hot/boiling water and / or an acid like vinegar. +40 year old nylon that has been exposed to UV, freeze/thaw/heat etc. may lose additional integrity when subjected to dyeing.
