Seattle has a variety of building programs and funding sources...buying old hotels for new homeless housing, redeveloping old public housing campuses, funding non-profits who build new low-income housing (including a $40m/year levy)... There's way too much to cover here.
Yesler Terrace is the closest campus redevelopment to the CBD, on First Hill overlooking the south end of Downtown. It used to have 561 family-sized units on about 30 acres, and it'll soon have more like 3,500 with maybe 1,100 affordable (mostly family-sized). The affordable units and most of the market-rate are in the six-story range.
https://www.seattlehousing.org/about...yesler-terrace
Several non-profit housing developers/owners live on levy dollars, grants, tax abatements, etc. Their projects tend to be centered on the Downtown fringes or other transit-heavy areas. Some of the big ones include
LIHI,
Bellwether,
Plymouth....