Sunshine,
Not sure what is available in Cary but the Salvation Army has helped many in similar situations. Perhaps other homeless ministries such as Sojourner's Place......
I can feel your heart going out to these folks, but Hechosedrugs is correct on all counts and unless you have money and time to burn, do not consider any co-signing for apartments -- don't ask how I know that, just accept that I do.
A quick Google search of "Cary, NC homeless shelters" yields this group which looks like a likely bet or at least a good source of information / referrals:
https://www.raleighrescue.org/about-us/ "We offer emergency overnight shelter and residential recovery for men, women and women with children." Good luck.
Keep coming back,
Jim