This happens every single time the poor get any sort of money. In poor neighborhoods the rents cost as much as people are able to pay, no more, no less.
Do you know when most rental deposits are collected? Around the tax return season.
If suddenly the poor had some money to spare - the rents will simply go up. The water bill will go up. Electricity, gas. Etc.. until there's no extra income left. And then the poor will be in exactly the same situation as they are now.
Source: long time resident (and landlord btw) of poor neighborhoods of Philly.
P.S: Government is willing to help poor with mortgages? House prices balloon. Government is helping with education grants - colleges raise tuition. Borderline-broke municipalities with enormous unfunded liabilities are looking for any opportunity to collect back taxes and make up new ones. I can go on.
Why would this be any different? As the history shows it will provide a benefit for only a short amount of time until costs catch up.
P.P.S: I am not an opponent of helping poor, quite the opposite. I just don't know how to go about it in real world.