RS if you are over 65

You may be thinking of SCRIE, which begins at age 62 but is only for low-income seniors:
http://www.nyc.gov/html/dof/html/property/property_tax_reduc_drie_sc_te.shtml

SCRIE is NYC taxpayers covering the annual escalations in these seniors' regulated or stabilized rents.

See also: http://www.housingnyc.com/html/resources/seniors.html

Even under SCRIE your rent goes up. It is just that the City pays
the rent increases/.

My co-op's sponsor has one qualifying tenant. (Household income less than $29K, with rent over 30% of that.)

The tenant's rent is frozen at $990 (more than 40% of their HHI) and the $340 benefit is crdited against the co-op's taxes.

There is an allusion to this concept in the Times article on the sand castle residents:
"Mr. Anderson’s rent rose to $1,100, but he paid only $430 a month; the balance was covered by the state, which also supported many of the complex’s nearly 2,000 other residents, who included Russian and Latino immigrants, veterans and battered women. About one-third were elderly or disabled."

SCRIE only supplements rent for people over 62 with limited income (perhaps the disabled are eligible as well I am not sure). The remainder of subsidized renters at Sea Girt Towers were probably Section 8, low income housing voucher program.

the program for the disable is called DRIE