Bucky's parents, Josephine Kephart and Barry James Kephart Sr., claimed their son had disappeared after leaving an note at their apartment in the 300 block of Texas Street southeast in Albuquerque, New Mexico on August 22, 1981. The note stated Bucky was going out and would be back soon. He has never been heard from again. He was not reported missing for two days.

Investigators believe Bucky was murdered by his parents. His sister, Beverly, who was twelve years old in 1981, stated that due to his dyslexia, Bucky could not have written a note as his parents said he did. She remembers hearing her brother being severely beaten by Barry Sr. the night he disappeared; she did not tell the police about this for thirteen years. Beverly stated her parents abused all their children in 1981 and Barry Sr. was an alcoholic. Authorities believe Bucky died as a result of the beating his sister overheard, and his body was put in a dumpster near the family's apartment. They do not believe it will ever be found.

Josephine died in 2005; Barry Sr. lives in Farmington, New Mexico and maintains his innocence in his son's disappearance. It is unlikely that anyone can be charged in Bucky's disappearance, as the statute of limitations has run out. Foul play is suspected in his case due to the circumstances involved.