On SS - this is pretty easy - for those not willing to look it up...
SS as mentioned - you have to work minimum 10 years. Your actual wages - or "Average Indexed Monthly Earnings (AIME)" is calculated based on your highest 35 years, and those years are adjusted for inflation - so its not always your most recent 35 years, but for most it is. So in the example of someone that worked 10 years, they would have 25 years of zero's added to their AIME.
Once you have an amount, you need to have reason to collect. You either need to be retirement age, or disabled. If your disability is psychiatric in nature, which for many homeless it might be, then you would need a diagnosis and a physician sign off. Its possible that many homeless are possibly eligible but maybe haven't gone through the proper steps, or don't want to see a doctor or whatever.
One last note. Social security is actually progressive - meaning the less you pay in, the more you get back, relatively speaking. For example if you worked minimum wage for 35 years, vs paid max SS tax for 35 years, as a percentage of pay in the minimum wage earner would get more back relative to their salary. So if someone is only getting $200, then they paid in basically nothing.
As for the OP - this is why I have become pretty much cold hearted as I age regarding those less fortunate. Everyone looking for a hand out, whether they need one or not. I know I shouldn't be this way, and wasn't always. I am always happy to help a friend no matter how much is needed. But I have no use for people like the old lady in the OP, and given she is training her grandchildren the same thing, there bloodline will likely always be takers.