Toilet valve black rubber seal disintegrating
It's unclear exactly where this seal is without pictures, but in general they are all replaceable, ease of replacement varies (sometimes you have to take the tank off the toilet to replace seals), and you had better try to find one made for your specific brand/model of toilet, as between manufacturers there are often incompatibilities. An actual plumbing supply may have a better selection of parts than a big box store.

Some replacement seals are offered in a "chlorine resistant" rubber formulation (often red) but in general, rubber at 30-50 years old does simply tend to fail from old age. If you are one of those people that puts an extra-chlorine "toilet cleaner" in your tank, you might expect to have faster aging of rubber and plastic parts as a result. Even if you do not add extra chlorine, they do not last forever.