You have not. You've shown that after a year of not buying lottery tickets they might have that $500, with the caveat of the fact that we know that's not really how that works - any savings gets wiped out by the next unexpected bill long before that.
> If I give them another $500 why wouldn't they just spent that too?
Where was that suggested? That's a silly approach to the problem.
Far more comprehensive solutions are necessary. Better housing policy, living wage, national healthcare, better regulation (or banning) of payday loans, guaranteed access to banking services, etc.