A Nassau County jail inmate died Monday, marking the sixth custody fatality this year at a time when the East Meadow facility’s private medical provider has come under intense scrutiny after allegations of negligent care.

Sheriff Michael Sposato on Tuesday identified the inmate as Michael Cullum, 62, and said the preliminary indication was the man had died of heart failure.

Records show Cullum had been jailed on drug charges after his Aug. 26 arrest.

The sheriff said Cullum came into the jail Aug. 27. The jail’s embattled medical provider — Armor Correctional Health Services — sent the inmate to the hospital Friday, where he remained until his death, according to Sposato.

The sheriff said he didn’t know the initial reason Cullum went to the hospital or enough about the specifics of his case to comment on the care Cullum received at the jail.

The state Commission of Correction said Tuesday it would investigate Cullum’s death, as it does all jail custody fatalities.

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“He should not be dead right now,” Dorothy Cullum, 57, of Glen Cove said Tuesday of her brother. “If they gave him his medication like he should have had, he would still be with us right now.”

The family’s attorney, Frederick Brewington of Hempstead, said Cullum suffered from chronic health issues, but went for more than a week without “his lifesaving medication” and was “basically tortured by those that had him in captivity.”

Brewington said the Cullums were demanding a full investigation of the death, and added: “There’s no reason, even though someone is accused of a crime and placed in custody, that they should lose their lives because of lack of medical treatment.”

Armor spokeswoman Yeleny Suarez said in a statement Tuesday the company had been notified an inmate who was admitted to Nassau University Medical Center on Friday had died.

But she said the company “cannot comment further on the patient’s health” due to a medical privacy law.

The state commission previously found Armor has provided inadequate care in connection with five inmate deaths since the company first won a Nassau contract in mid-2011.

New York Attorney General Eric T. Schneiderman sued Armor in July, saying the company has provided “woefully and dangerously inadequate health services” while continuing to collect millions of dollars in public money.

In addition, Schneiderman’s office has said four of the previous five inmate custody deaths in Nassau this year “raise serious concerns” about Armor’s care.

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Armor has repeatedly defended its medical practices and has said it will fight Schneiderman’s lawsuit.

The company and the county also are fighting federal lawsuits from the families of four Nassau inmates who have died since 2011.

After Schneiderman’s lawsuit, Nassau Comptroller George Maragos said he wouldn’t pay Armor’s bills going forward until the company provided data showing it was meeting contract performance standards.

The comptroller so far has refused to pay Armor’s July and August bills of about $1 million each, and a Maragos spokeswoman said Tuesday those invoices and their accompanying data remain under review.

Armor recently said it wouldn’t bid to renew its contract, which ends in May, and also signaled it could pull out of the jail early if the county breaches its contract by not making payments.