You can find listings for any geographical area on the govt. site for HUD.
Some people think that the only rental options are with a Section 8 voucher. Those have long waiting lists depending upon population density.
However, there are subsidized apts. for Seniors. In this case the section 8 designation is for the building rather than the individual renters.
Some buildings have long wait times but others do not. It really depends upon each building. You can get a complete booklet of listings for the area and then apply to the buildings that fit their needs.
When living in subsidized housing, the rental amount cannot exceed 30% of their total income. This is a very affordable option for those on low fixed income.