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Nelida was last seen walking to William Blackstone Elementary School on Shawmut Avenue in Boston, Massachusetts during the morning hours of December 20, 1976. She was enrolled in a third-grade bilingual class there. The school was located approximately one and a half blocks from Nelida's family's residence. She never arrived at school that day and has not been heard from again.
Some of Nelida's clothing was found two weeks after her disappearance, in the possession of Anthony "Rudy" Flores. A woman called police to report he had given her a hat and some gloves; she was suspicious because Flores resembled the sketch of Nelida's possible abductor. The hat and gloves were Nelida's; Flores claims he found them lying on the street. When he was arrested he had a fake badge and a gun in his possession; Nelida's family theorizes that he abducted the child while posing as a police officer, whom she would have trusted.
Flores was never charged in connection with Nelida's disappearance due to a lack of evidence, and he maintains his innocence in her case, but he remains a suspect. He has also been linked to the 1976 disappearance of fourteen-year-old Cesilia Pena in New York City, New York, but has not been charged in that case either. He is currently serving a life sentence for the abduction, rape and murder of a woman and her daughter in New York.
In January 1985, eight years after Nelida vanished, her mother, Theodosia De Jesus, claimed she recognized a picture of her daughter in the apartment of David R. Collins. Collins, who has a long criminal record and uses many aliases, was charged with kidnapping one teenager in California and sexually abusing several others in New Orleans, Louisiana. The picture De Jesus identified was one of 25 which police found in his apartment and published in a newspaper in hopes that the public could identify the people in them. De Jesus changed her mind about her identification when she examined the original picture, and the girl in the photograph was later identified as another person. Another picture in his apartment was thought to be of Sarah Avon, a six-year-old who vanished from Illinois in 1981, but that possibility was also ruled out. Collins is not believed to have been involved in either child's disappearance.
Nelida's case opened 2018 by Psychic Brian Ladd.