Diella Beth Ludwig and her twin sister were born while their mother lived at the state’s Lowell Correctional Institution. From there, state child welfare administrators sent them to live with their father, an unemployed, drug-abusing 24-year-old with a long criminal history and a prior report concluding he should never be left alone with children.

Bothered by the fussy, underweight baby’s crying, Thomas Ludwig crushed Diella’s skull. She wasn’t even 2 months old.

The state Department of Children & Families was so troubled by Diella’s death that administrators strengthened a policy requiring staff to look closely at infants born to parents already under an abuse or neglect investigation. They called it the Ludwig Protocol.

But when Emma Morrison was born late last year to parents with a long history of drug abuse and domestic violence, the Ludwig Protocol was ignored . Now she, too, is dead.

Although there is no evidence Emma met such a violent fate, DCF, the Palm Beach County Sheriff’s Office and medical examiners are investigating the murky circumstances of her Jan. 17 death. No one has been charged, although police found a crack pipe in plain view when they entered the house, a source told the newspaper.

Emma was the same age as Diella.

Emma’s death raises troubling questions about lessons learned and not learned, even as DCF launches the most recent of many agency-wide reforms designed to better protect children.

Emma had lived 49 days. She spent 34 of them the subject of a DCF investigation into her welfare.

Though Emma’s parents had been the subject of more than 10 prior reports to the state’s abuse hotline — and four other children had been taken from the mother by the state — child welfare administrators did virtually nothing after receiving a report that Emma had found herself smack in the middle of a physical altercation between her parents.

Authorities refused to discuss Emma’s case. Chief Medical Examiner Michael Bell would not disclose her name.

Neither of Emma’s parents could be reached by The Miami Herald.

Emma’s death occurred less than a week after Hallandale Beach police found a tiny skeleton buried behind a house where, three months earlier, DCF had ignored a report that Dontrell Melvin had disappeared 19 months earlier. No one — not his parents, not police, and not DCF — went looking for the infant, who apparently vanished when he was about 5 months old. Authorities have yet to determine whether the bones belong to Dontrell, who would now be 2.

Though Emma’s mother, 33-year-old Lisa Lamoureaux, had a long history of drug abuse and arrests — and had permanently lost custody of all four of her children — the extent of DCF’s intervention after her latest birth was to refer her to parenting classes and other services that either were unavailable or that she rejected.

Reports show investigators failed to inquire whether Lamoureaux was still using drugs, failed to interview her neighbors or family members, and failed to seek the advice of their own lawyers regarding the best way to protect Emma.

Referring to DCF’s most recent reform effort, called the Child Protection Transformation, DCF’s top child welfare attorney, Mary Cagle, wrote in a Jan. 24 email: “With the transformation project I am hoping we can change this culture.”