A few hundred to $1K seems too little to have much impact.
Going from 0-$1k/mo or $1K to $2k/mo means you're still broke.
You can definitely afford some food or necessities that were harder before, but fundamentally, you still need to hustle to change the fundamental financial situation.
I would still have expected that going from 0-1K to 1-2K would allow a lot more people to bootstrap themselves out of poverty. At least under the hypothesis that Poverty is a symptom of a persons circumstances, with most notably a lack of a financial buffer allowing for smart moves (e.g. the Sam Vimes theory of boots, or not being able to get a job because you cannot afford transportation).
In that case, that extra money should likely cause quite a few people to get out of those self-reinforcing poverty traps, and let them escape.
Going from 0-$1k/mo or $1K to $2k/mo means you're still broke.
You can definitely afford some food or necessities that were harder before, but fundamentally, you still need to hustle to change the fundamental financial situation.