Compare/contrast roles the prison system, the family, and the social stratification system play in contributing to or alleviating the problem of crime
The problem with prisons is that they are designed to contain and punish, not to rehabilitate. People can only be in prison for so long, then they are released back into society. Since they don't know any better, they often commit the same crime or another crime and return to prison.
Wow. That's a big question. If the issue is alleviating crime, one of the three elements you mention does the least to impact the prevention or repetition of crime. That, of course, is the prison system. Prisons, it's pretty clear, do not prevent criminal behavior. There is seemingly no deterrent to the threat of a possible prison term--and that goes for the most minor crimes to the capital crimes punishable by death. In fact, I'm guessing a case can be made that the threat of prison as a punishment is laughable to many would-be criminals. It's a risk many are willing to take, obviously. None of this threatening or punishing has alleviated crime, nor will it as long as prisons are not rehabilitative--which I'm not sure they ever will or even should be.
So, if the prison system is not a factor one way or the other in criminal behavior, what is? Family and social stratification are the two you mention, and I'm sure they are the top two factors in determining whether or not someone turns to crime. The family is certainly fundamental in creating well adjusted, law-abiding citizens. If the expectation is that rules will be followed, even at an early age, the lesson is being taught--obey the laws to which you are subject. That's often easier to enforce when a family is intact (simply because two parents speaking with one voice have more impact), but it only takes one parent or grandparent to set that standard and expect the children to live to it. From there, people make their own choices.
Finally, social stratification--by which I assume you mean the economic and social conditions which separate members of society from one another--is probably the biggest contributor to crime. The "haves" are not generally involved in criminal behavior while the "have nots" are more likely to do so. That's a grand simplification, I know, but I think the statistics prove me right. So, it's not the people or the system nearly so much as social stratification (which I'd probably call environment) which contribute to crime.
The prison system neither encourages criminal behavior nor stops/deters it--except for its ineffectiveness. Families generally discourage criminal behavior and rarely promote criminal activity. That leaves the issues of social stratification: poverty and homelessness and joblessness, all of which lead to helplessness and even desperation. And, other than crimes of passion or thrill-seeking, helplessness and desperation are two of the greatest motivators for criminal behavior.