Uncle Sam does not build a complex himself for low income family, it is the investors that using one of the low income housing program to build such project.
you need to find out what program was it build with, section 8? Farm Home Credit? senior housing? or the newer LIHTC?
The Low Income Housing Tax Credit (LIHTC or Tax Credit) program was created by the Tax Reform Act of 1986 for low- and moderate-income household, usually investors use either tax free bond or private loan to build the project and the project will receive a tax credit equal to 90% (Private funded project) or 40% (public funded project - tax free bond) of their hugely inflated cost (one project I saw was 95k per unit in Indiana, and that is crazy) over a 10 year period, most of the time, the owner of the property will not be able to use all of the tax credits, and therefore, many LIHTC properties are owned by limited partnership groups that are put together by syndicators, the sell the tax credit on 75 cents for each dollar to companies and private investors to against their federal tax liability in return.
there for, in 10 years, the project is paid for by the tax payers, and the project owner make millions on selling tax credit and still own the project, then at the end, they sell the project thru a non profit group to a third party buyer and still don't pay a dime in taxes on capital gain.
I did a lot of research on tit year ago, on one project I saw, 132 unit complex cost 12 mil, the developer makes 2mil in the beginning, builder makes 1.5 mil and each year tax credit can sale for almost 1mil, now that is huge money, but this market is dominated by big guys, they knows all the network and channel, they build project one after another, they really do not care about renting the units, because they make their money by selling tax credits.
80% of the apartment complex build today is under this program.