It's true that the spending of the poor tends to be concentrated on the "basics": food, housing, transportation, childcare, utilities. Such a situation is inherently subject to more pricing risk. Relatively wealthier people might forego cable TV for six months in order to pay for unexpected car repairs, but that wouldn't be an option for someone who doesn't have cable TV in the first place. Still, your objection has it backwards. Yes, the poor face a relatively limited range of choices in how they can live in an arbitrarily unfair society like ours. However, increasing the income of the poor increases their choices, period. We don't know in advance how exactly they will react to this increased choice, but it's extremely unlikely that their reaction will be to give all the extra money to the same asshole landlord. A more reliable car might allow a family to live in a completely different neighborhood. Working a single job instead of two might allow a parent to spend less on childcare. And so on. Poor people are humans with imagination, not rent-payment-maximizing automatons.
I don't claim to know anything about your town, but I've lived lots of places and in general, in order to really fuck people over the bastards first have to limit their freedom somehow. Are there only certain parts of town in which the poor are allowed to live? Has public transportation been limited in arbitrary ways? Do zoning regs or HOAs enforce impractical restrictions on housing? Would it be OK if your neighbor parked a mobile home and camper behind her house for her recently-divorced sister-in-law plus five kids? What if her nephew and his girlfriend also moved out back?