Question: The issue has crept up on me slowly over the last several years. I am increasingly aware of the massive debt that many of my students are taking on, debt which is far beyond the sort of debt that I incurred as an undergraduate in the 1980s. Because of this, in recent semesters I have found it somewhat difficult to fail students. Instead of simply asking myself "does this student deserve to fail this class?", I find myself asking "does this student deserve to have their life ruined?" In many cases (e.g. students who are already on academic probation) this is not much of an exaggeration. It is a very bad situation to find yourself in your early 20s with no college degree but $30,000 in debt. In some cases, I am aware that a decision of mine might be a contributing cause of a student ending up in just such a situation. I can no longer regard a failing grade as a relatively minor matter (like a speeding ticket).

How do professors reconcile their de jure role as guardians of academic integrity with their de facto role of being (at least in part) responsible for their students' economic future?

Answer: 
Your compassion is admirable but is not unique. Other answers have provided more detailed answers about grading, content prep and presentation, students 'earning' their grade and that is all true. 

Responsibility vs Accountability
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With my answer I want to add to the discussion the point that the economic situation of a student may seem dire it is still the students responsibility and not yours. Them making you aware of their situation (even innocently) can have the effect of shifting that responsibility unfairly to one who is not accountable for it (you). 

It's Not Life or Death, Until It Is
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When I was in college there was a professor who would comment about students complaining about difficult tests or mounds of homework by recalling how different it was in the 1970's when a male student failing out of college made them eligible for the draft with a likely outcome of being sent to Vietnam; which carried with it a very real risk to their health or lifespan. He wasn't saying that he failed people in order to send them to be drafted, he was saying the motivation of students facing such risks were much higher in those days. It wasn't him that decided who was born male, who would be drafted, who would be given a gun and sent out into the jungle.

Guilt, party of 2
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Did the student confer with you before choosing their major? Did they ask your opinion about which school to attend? Did they check with you before taking out those loans? You are neither responsible nor accountable for their choices.

Advice
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While I would not ask you to stop feeling compassion, you should not allow their predicament to turn into guilt on your part. Should you turn your back on these students? Absolutely not, but what then?

Either add something in your syllabus or to your first lecture something to effect of, "I know some of you may be relying on financial aid (loans, scholarships) which carry an eligibility component which may be affected by how well you do in this class. If that applies to you, I would suggest you get with me early in the semester so I can assist however I can to point you to resources to improve your chances of success in this class." 

To effect, you are saying "I can point you to water but I can't make you drink". That is the most that can be reasonably be asked of you since you can't do the work for them or make them attend class, etc.
I generally design my exams so that even a student with relatively limited understanding of the course can pass. I would really only consider a student who has achieved the highest grade (> 80%) to have a good understanding of the material, and I often see just-passing exams (50-60%) where I think that the student really had no idea, but somehow managed to scrape together enough marks to get over the line.

Armed with that viewpoint, when I see a student who fails, I think they must have really deserved it! So I don't feel too bad about failing them; they need to put in some effort to fail my course!