Many of the grants/ad you see are things like 10k to go to college. It's technically correct, it's the pell grant which is given to poor college students. Yes if you attend a city college, fill out a fafsa and qualify the school will give you a check (the balance of the pell grants after tuition), the check is to cover things like books and help cover expenses.
Similar is the americorps/senior corps/job corps program, which in exchange for volenteering you can get a grant that you can put to tuition or use for school-related expenses (example I put in 450 hours in 2 years and got 12,500 knocked off my tuition, for teaching english phonics to spanish speaking children, and the school could use me as an free intern instead of finding money for a new aide).
Another sort of grant is the one we have here for preschools to upgrade pre-1975 buildings (the asbestos & lead paint era ones). The cash covers the remodel to bring to current safty standards, a similar one to replace worn-out playground equiptment.
So yes there are grants, but you have to actually DO something to qualify.
Most, if not all appily to small businesses, college students (who can get free childcare if poor enough, same for welfare-to-work programs), fixing up a home would be stuff like energy credits, which come off your taxes if you upgrade to energy star stuff (here the utilities run a program where if the appliance is more than 10 years old they'll replace it, again if you're broke enough).