The former vendor at the Nassau County jail reportedly is responsible for three inmate deaths.
Newsday, citing findings from the state's Commission of Corrections, claims Armor Correctional failed to provide adequate treatment for the men last year.
A claim with Armor denies.
The county and Armor are currently fighting four federal lawsuits connected to other inmate deaths.
Earlier this year, officials reached a deal for NUMC to take over medical care at the jail.