They just give up. Period.
My husband drew my attention to a new study published in the April issue of Psychological Science in which researchers provided low-income Chicago 7th-graders in two randomly selected classrooms with one of two kinds of information: Classroom A received information about need-based financial aid opportunities, indicating that college was a possibility for them while Classroom B was provided information about the enormous costs associated with a college education, indicating that college was not a viable option (specifically they were told that the average college tuition costs $31,160 to $126,792).
The researchers then assessed students' motivation levels and mentality towards school using questionnaires about goals, grades, and time usage.
The students in Classroom A expected to do better in school and planned to put more effort into studying and homework, compared to the students in Classroom B, who did not view college as a realistic possibility.
In a sensitivity analysis the researchers repeated the study with Detroit classrooms, and changed the second condition from info about college costs to no info at all. Results again indicated that students provided financial aid information had a more open mindset toward their future.
The authors conclude "part of the reason children begin to fall behind is that effort in school is understood to have meaning only when it leads to a path to the future. When the path to college feels closed because of a lack of financial assets, school-focused aspirations and planned effort suffer."
For more, see the work of Daphna Oyserman, University of Michigan.