That may be true in some countries, but not in America.
In America you have to actively refuse help in order to be in continual pain or homeless.
I HAVE been poor, there is no excuse for hunger or suffering in the US, there are programs to help.
The problem is not that they are poor, its that they don't want to be helped, the reason for this could be any number of things from simple depression to severe mental disorders, but it IS NOT because help is unavailable.
A severe tooth abscess can be handled by the ER if its that bad and no publicly funded ER will turn down you down, its illegal. I know, I've been in EXACTLY that spot. And for reference, alcohol does pretty much nothing at all for tooth pain, you're far better off packing clove powder around it to numb it and treat the infection than drinking yourself silly, unless you drink enough to pass out