The original document is called an income share agreement (ISA). It's not a debt instrument or a loan, but is actually a legally binding "equity" stake in a student's future income under specific circumstances for a specific amount of time. Lambda, for example, takes a percentage of income for two years, only if they're working in a software-related field, and only if they're making above $50k/yr. We also cap the amount paid over the two years at $30k, regardless of how much a student is making. So, yes, if they don't get a good job, we never get paid. That only seems fair.
As for how it works practically:
In conjunction with the ISA, each student signs a 4506-T or 4506T-EZ (or any successor form) with the IRS, which effectively copies us on their taxes.
Students self-report their salary, and we adjust payments according to their reports, until year-end reconciliation, which happens around tax time. We get their taxes and double check that their self-reporting has been accurate, and adjust accordingly.
Should a student default, we have the same remedies that any other private lender would - we reserve the right to report to credit bureaus, we can sell the agreements to collections, etc.