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: 
The other answers are great, but I want to stress one thing not really mentioned in other answers: **if you are concerned, talk to them before they fail**. Don't single them out for help because again it won't be fair, but still: tell them explicitly that if they continue performing as they have, they are going to fail the class. Point them to the various resources that are available (e.g. undergraduate tutors, office hours). If they still fail, as the proverb goes, you can lead a horse to water, but you can't make it drink.
Here in Germany universities are quite strict. After my daughter failed the very last maths exam three times, she was out.

However, strict does not mean heartless or planless. Her uni had an arrangement with the tech unis; one of them agreed to accept the exams she had already passed and enrol her in a similar course, for the third year. She was not alone in this.

This way all that time and investment was not lost.

You could organise a similar scheme with nearby polys or tech colleges, to take up your students, who didn't quite manage, but are still worthy of education. So everybody wins.