WASHINGTON — When Congress created a student loan forgiveness program in 2007, lawmakers wanted to draw people to vital but relatively low-paid careers with a promise: after a decade, if borrowers faithfully paid their debts and pursued their work, they would have the remainder of their student loans written off.

Since then, tens of thousands of graduates were led to believe by their student loan servicers that they would qualify for relief at the end of a decade, only to be shocked when their applications were rejected.

The blame can be spread broadly — to loan servicers who at best failed to inform borrowers of what was needed to qualify, to the single company in charge of the program that has been repeatedly cited for shoddy service, mismanagement and poor record keeping, to lawmakers who wrote in a baffling list of requirements, and to the Education Department, which has failed to step in and correct the problem.

Those affected are people like Kelly Finlaw, who, for a decade, dreamed of small splurges: a new shower head that did not spray everywhere but her bathtub, coffee from a cafe — maybe even an apartment she would own, rather than rent, near the school where she worked in New York. All of that would be possible, she had thought, once the federal government forgave her student loans.