Ineligibilty because of criminal activity: 24CFR 960.204...
Public Housing Authorities are required to Prohibit admission to families who's members have shown a pattern of use of illegal drugs, who are currently engaging in illegal use of drugs, whose abuse of alcohol or pattern of alcohol abuse would interfere with health, safety or right to peaceful enjoyment of other residents, or those convicted of drug related criminal activity.
There are mandatory federal rules in regards to criminal/drug activity and then each Housing agency may have other adopted rules which are permissive. The rules would apply to admission qualification and apply to continued occupancy.
HUD regulations that govern admissions can be found at 24 CFR 960.203, Public housing lease regulations 24 CFR part 966 as amended by the Final Rule on Drug Abuse and other Criminal Activities published in the Fed Regs May 24, 2001, Lease requirements imposed by state law and reasonable lease requirements by the PHA.
Bottom line the person has the decision to sign the lease or no...Don't sign the lease if you don't wish to play by their rules.