Shelter is another story, but as long as you provide a means to assign some of your BI ahead of time to a provider (landlord), this should also be a minor issue outside of the very mentally ill, who are going to be screwed in any system (including the current one) that doesn't take them under involuntary managed care.
When I say assigning your BI, I mean being able to go through a process on the spot that guarantees a landlord $x over y weeks from your BI in exchange for y weeks of tenancy, possibly with additional penalty fees the landlord can claim for any damage to the property. Essentially, a lease without the need for a security deposit or credit check. I'm certain you'd have quite a few places willing to take in renters with guaranteed rent coming in at regular intervals.
But my point is, when you hand someone a check and they must in turn be responsible for spending that money on food and shelter, they might not actually do that and then what? At least with Section 8 and food stamps you're earmarking the money for a particular purpose so as to make it much harder for the money to not be used the way it was intended.
> WRT things like the car breakdown case you described...
Keep in mind "my car broke down" is a metaphor for any unexpected event that impacts someone financially (and commonly as an excuse for "I spent my money foolishly and now I'm broke"), so I didn't mean for that to be some single concrete case I wanted a specific answer for. But again, if we decide that we need to help someone on BI who had some particular financial hardship beyond what their check allows for, how do we police that?