Blackening of finger/toe nails is a usual complication of prolonged Diabetes.
When blood cannot travel freely throughout the body, your cells cannot survive, infection can develop, and tissue can die.
Diabetes hampers blood flow as well as affects sensation in the limbs. So your dad might have been hurt and not even realised.
You should have it checked by a doctor right away so that it can be appropriately treated. Your father needs to see his Diabetologist/physician to make sure his Diabetes is well controlled too.