I have an add-on question. How true was it that the average person 'could barely afford to live'? I've heard anecdotal stories from older relatives of small southern towns being basically unaffected by the depression.
I think you are going to need a state by state answer. Statistically the number imprisoned almost doubled during the great depression. But congress passed laws to limit the selling of goods produced with prison labor (Notably the Hawes-Cooper Act). But I don't have enough knowledge to address how these twin stresses on the prisons and the prison population were dealt with in any particular locale.
Here are a few sources:
http://www.encyclopedia.com/article-1G2-3408900129/hawes-cooper-act.html
http://law.jrank.org/pages/1782/Prisons-History-Modern-prisons.html
BTW, this period saw the growth in black men being incarcerated grow three times faster than the general population so a state by state analysis should probably consider the racial differences in how prisoners were treated.
This question was asked and answered last year. Here is a copy of the top comment. by /u/leisure-lee
The Great Depression's incarceration rates were the highest the nation had seen yet. The incarceration rate for federal and state prisons peaked at 137 per 100,000 in 1939. Rates dropped with the beginning of WWII as jobs and military service set the country back on the economic track.
The prison system, in reaction to the rising incarceration rates, responded with a parole system. Known as the Second Great Experiment, it was believed that putting the prisoners to work and/or teaching them a skill would improve them to make it society as a law-abiding citizen. For example, prisoners might be employed to make burlap sacks or in fields to collect foodstuffs. The income went back into the prison system. Once the inmate had proved his transformation, he could be placed on parole.
I should also note that the majority of crimes were actually more violent crimes of passion and those related to prohibition. It would be foolish to think that theft was not a problem, but battling the more serious felonies were given priority. Facilities, such as Alcatraz, held particularly dangerous inmates apart from the lesser offenders.
Though I have yet to find an account of some one trying to get into prison, I can't imagine this was the course for many, if any, persons. The environment of prisons were extremely unpleasant, low on supplies, uncomfortable, and brutal. Rape, gangs, and abuse from guards and prisoners alike were rampant.
http://monthlyreview.org/2001/07/01/prisons-and-executions-the-u-s-model/
Not sure if its the location you were thinking of, but it was a common practice in many smaller Canadian towns for the homeless people who rode the rails to ask to spend the night in the local jail, where the personnel often gave them some amount of food, though that was a choice. This was particularly common in the winter to avoid the potential of freezing to death.
Source: Pierre Berton, The Great Depression.
I think I could likely answer the question posted by OP and a few others asked in this thread. However I know this sub is not a place for generalization or facts that are unsupported but I did go to undergraduate and graduate in which undergrad I studied the US penal system pretty extensively and did work in sociology in grad school with populations that most often parts of the American justice system. I'll try and put some stuff together to try and help but it may take a few hours.