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://www.triquarterly.org/reviews/doing-time-depression-everyday-life-texas-and-california-prisons-ethan-blue

http://monthlyreview.org/2001/07/01/prisons-and-executions-the-u-s-model/

This question came up a while back and I think my answer from that post still stands. In particular the desire to avoid jail, which inevitably meant hard labor and left you no better off than when you went in. Here's that answer:

If you were looking "3 hots and cot" during the Great Depression, getting picked up for some "small crime" might be an option, but certainly not a good one. Take vagrancy, for example, during California's "Bum Blockade" in the early 1930s those arrested were given a choice of "either leave California or serve a 180-day jail term with hard labor."

Studs Terkel in Hard Times: An Oral History of the Great Depression similarly records one Louis Banks talking about his run-ins with the law as a vagrant:

I was in chain gangs and been in jail all over the country. I was in a chain gang in Georgia. I had to pick cotton for four months, for just hoboin' on a train. Just for vag. They gave me thirty-five cents and pair of overalls when I got out. Just took me off the train, the guard. 1930, during the Depression, in the summertime, Yes, sir, thirty-five cents, that's what they gave me.

I knocked on people's doors. They'd say, "What do you want? I'll call the police." And they'd put you in jail for vag. They'd make you milk cows, thirty or ninety days. Up in Wisconsin, they'd do the same thing. Alabama they'd do the same thing. California, anywhere you'd go.

Maybe if your situation was so dire that hard labor and terrible (if relatively) consistent food was preferable, then you might see getting arrested as an improvement. A consistent theme running through hobo stories, however, is that they were out there looking for honest work; serving a few months of hard time wouldn't leave you any better off then when you started.

A better option was when various New Deal programs started setting up work camps. From Hard Times again, an Ed Paulsen happily recounts his time in a transient work camp:

They drive us up to an old army warehouse. They check you in, take off your clothers, run them through a de-louser, and you take a bath. It's midnight. We come out, and here's a spread with scrambled eggs, bacon, bread, coffee and toast. We ate a great meal. It was wonderful. We go upstairs to bed. Here's a double-decker, sheets, toothbrush, towels, everything. I sat down on this damn bed, I can't tell you, full of wonderment. We thought we'd gone to heaven. Hal's a young punk, he's seventeen. He said, "What the hell kind of place is this?" I said, "I don't know, but it's sure somethin' different."

Studs goes on to note that Ed was assigned a job with the National Youth Administration (and eventually with UNICEF). Ed says of that:

The NYA was my salvation. I could just as easily have been in Sing Sing as with the UN.

In conclusion:

• Getting arrested for even a small crime meant you could look forward to jail and hard labor, which have always and will always, suck.

• Getting into a New Deal labor camp meant getting a place to stay, food to eat, and a job to give you meaning. Vote FDR in '36.

Follow up question- how were the conditions in the average prison (for an average prisoner) in the U.S. at the time?

In his book, "Breaking Blue," Timothy Eagan mentions that police officers in Spokane, Washington, tended to be ex-loggers, and were hired for their ability to deliver a beating. The idea being that the police department was going out of its way to avoid putting people in jail, (where the city would have to feed them.)

They'd beat people up for infractions, and either have their friends haul them outside city limits, or the police would throw them in an empty boxcar on a train leaving town.

Eagan interviewed a lot of people from that era, including police officers, in the course of investigating the role of the Spokane PD in a butter robbery and subsequent murder of a town marshal.