Earlier quoted context omitted.
there is a cliff, such that a the 2 adults, 2 children on 22,500 gross income may have access to $48,700 after refundable tax credits, SNAP, housing, etc [linked in other comment]. However if that same household earns just $5,600 more annually nearly all of those transfers cease to be available and the total income accessible becomes $36,400. It really is a case where making more is too expensive. That's less than 11…
Additionally, people aren't stupid. That guy with a 22.5 HHI is actually working for cash on a concrete crew all summer, dealing weed, running scrap or some other source of under the table income that makes people above a certain tax bracket clutch their pearls. You often lose the ability to be competitive at such gigs when you take the time commitment of a "real job" even if only part time so there's that cliff too.
Working all summer on a concrete crew for cash seems like a good idea until an on-the job injury without workman's comp changes the way he walks for the rest of his life. Dealing weed doesn't have the profitability these days with legal dispensaries in many states and mandatory sentencing in the others. Running scrap is somewhat 'grand larceny adjacent', and again prone to an uninsured skill-saw event. Remember to wear eye protection when using a power tool.
So, returning to the two adults, two children exemplar household, it seems reasonable to expect that in general these people exhibit a lower incidence of these behaviours. If one or both of those children are still young enough to require round the clock supervision there is a significant limit on the couple's available working hours every week. That would make a similar 'hard to commit' to a higher paying full time job, for at least one parent.
I mean, the two kids really cut into the time flexibility necessary to participate in the grey-to-outright criminal economy, so I posit that people who report as earning the bottom quartile who also undergo the stringent documentation requirements necessary to receive benefits are more likely to be actually living on what they legally declare, than are somehow working, stealing benefits AND making substantially more through grift or crime.
I admit this may be my own biased observation, but the single 'smaht guy' with 22.5k household income and the criminal gig enterprise seems very unlikely to be filing a tax return or receiving any other support. So that case is interesting, but not very applicable in this equation: he's living on whatever he has this week or this month with very little long term benefit from earnings he cannot use to build a credit score, secure stable housing or invest in a future.