What causes the fingernails of an elderly person to seem to disappear?

Unsure what you mean: Nail growth certainly slows some with aging, but they should not be disappearing. Nails can be a sign of many conditions including vitamin deficiency, anemia, diabetes, as well as, disease of the heart, lung, kidney, or liver. Bottom line is that disappearing nails are not normal aging, and if you have noticed changes recently seeking medical advice n person would be a good idea.