Guards in Jeffrey Epstein's unit were working "extreme overtime" in the hours before his death, leaving gaps in his supervision, US media report.
The Department of Justice and the FBI have both launched investigations into Epstein's death amid questions surrounding the circumstances.
Epstein, 66, was denied bail and faced up to 45 years in prison on federal sex trafficking and conspiracy charges.
A post mortem examination into Epstein's death was performed Sunday.
New York City's chief medical examiner, Dr Barbara Sampson, said that more information is needed before the cause of death is determined.
Dr Sampson said that a city medical examiner conducted the examination on Sunday while a private pathologist observed, at the request of Epstein's representatives.
Corrections officers at New York's Metropolitan Correctional Center had been forced to work overtime to make up for staffing shortages, according to US media.
One of the corrections officers was reportedly on his fifth straight day of overtime shifts, while another guard had been forced to work overtime, Serene Gregg, president of the American Federation of Government Employees Local 3148, told the Washington Post.
"If it wasn't Mr Epstein, it would have been somebody else, because of the conditions at that institution," she told the newspaper.
"It wasn't a matter of how it happened or it happening, but it was only a matter of time for it to happen. It was inevitable. Our staff is severely overworked."
Ms Gregg said she did not know the details of the investigation but that she has long complained about the work conditions at the facility.
The guards failed to follow several protocols leading up to Epstein's death, according to the New York Times.
Epstein, who had been placed on suicide watch after his apparent suicide attempt last month, was supposed to have a cellmate and checked in on by a guard every 30 minutes. Mr Epstein was reportedly left alone early Saturday after his cellmate was transferred.
Epstein was arrested on 6 July on new sex-trafficking charges. The indictment alleged that he paid girls under the age of 18 to perform sex acts at his Manhattan and Florida mansions between 2002 and 2005.
According to the charges - which Epstein denied - the girls, some as young as 14, were given hundreds of dollars for sex acts.
Hundreds of pages of court documents unsealed on Friday - one day before Epstein's death - included new details of the sexual abuse claims against the multimillionaire, including allegations by a woman that she was forced to have sex with Epstein's powerful friends.
Without Epstein to stand trial, legal experts told BBC's US affiliate CBS News that federal prosecutors will likely dismiss the criminal case against Epstein.
Lisa Bloom, an attorney for several women who claim they were abused by Epstein, told CBS that she plans to file civil litigation against Epstein's estate.
Attorney General William Barr said he was "appalled" to learn Epstein had died.
"Mr Epstein's death raises serious questions that must be answered," Mr Barr said on Monday, adding that he has demanded a "thorough" investigation.
On Monday, two French government ministers also called for an investigation into Epstein, saying a US probe into the accused child sex trafficker had revealed links between Epstein and France.