My mom's(47) one of mandibular central incisors cracked into two pieces and one portion broke out, in which something black colored attached. help.

Dental decay: I suspect she had a cavity that weakened the tooth. When it broke, i think what you saw is the decay (cavity) of the tooth. See a dentist in the next day or two for care.

I would be less: Concerned about the color of the fragment & more concerned about controlling potential pain & infection. The description portrays a tooth that does not sound restorable by the dentist. Best to schedule a focused consultation with the general dentist to determine the tooth's fate. If the tooth requires extraction, which it sounds like it does, your mom may be a candidate immedite implant, .