The ones I'm thinking of are the Ashbury Dwellings, both the Northwest Co-ops, the Phillis Wheatley YWCA, Lincoln-Westmoreland, and Foster House. With the exception of the YWCA they also have parking lots, as a common feature. They serve different housing needs, such as women, and seniors and many take Section 8. None of them are claimed by DC Public Housing as properties.
The point of the excerise is awareness. It is easy to forget with the cranes and contruction of the pretty new market rate condos and apartments that such housing exists. Shaw is a diverse community and the non-market rate housing keeps a level of diversity in various aspects of Shaw life.
And this might just be me, but non-market rate housing is not a problem. Too much of it may be since concentrated poverty is bad. But I notice lately, problem places, that used to be big problems (ex. Lincoln-Westmoreland) are less so as the neighborhood as a whole has improved. Maybe this is the trick of having gentrification work for different kinds of people. If the affordable places can manage to remain, then the residents can have their quality of life improve because there are now more middle/upper income folks in their neighborhood demanding better policing, city services, etc. Yes, everyone in the District deserves better policing and city services, but I've learned it doesn't come without lots of demanding.