NEW YORK — Tens of thousands of people who took out private loans to pay for college but have not been able to keep up payments may get their debts wiped away because critical paperwork is missing.

The troubled loans, which total at least $5 billion, are at the center of a protracted legal dispute between the student borrowers and a group of creditors who have aggressively pursued them in court after they fell behind on payments.

Judges have dismissed dozens of lawsuits against former students, essentially wiping out their debt, because documents proving who owns the loans are missing. A review of court records by The New York Times shows that many other collection cases are deeply flawed, with incomplete ownership records and mass-produced documentation.

Some of the problems playing out in the $108 billion private student loan market are reminiscent of those that arose from the subprime mortgage crisis a decade ago, when billions of dollars in subprime mortgage loans were ruled uncollectable by courts because of missing or fake documentation. And like those troubled mortgages, private student loans — which come with higher interest rates and fewer consumer protections than federal loans — are often targeted at the most vulnerable borrowers, like those attending for-profit schools.

At the center of the storm is one of the nation’s largest owners of private student loans, the National Collegiate Student Loan Trusts. It is struggling to prove in court that it has the legal paperwork showing ownership of its loans, which were originally made by banks and then sold to investors. National Collegiate’s lawyers warned in a recent legal filing: “As news of the servicing issues and the trusts’ inability to produce the documents needed to foreclose on loans spreads, the likelihood of more defaults rises.’’

National Collegiate is an umbrella name for 15 trusts that hold 800,000 private student loans, totaling $12 billion. More than $5 billion of that debt is in default, according to court filings. The trusts aggressively pursue borrowers who fall behind on their bills. Across the country, they have brought tens of thousands of lawsuits in the past five years.

Judges throughout the country have tossed out lawsuits by National Collegiate, ruling that it did not prove it owned the debt on which it was trying to collect.

The trusts win many of the lawsuits they file automatically, because borrowers often do not show up to fight. Those court victories, which can be used to garnish paychecks and federal benefits like Social Security, can haunt borrowers for decades.

The loans that National Collegiate holds were made to college students more than a decade ago by dozens of different banks, then bundled together by a financing company and sold to investors through a process known as securitization.

These private loans were not guaranteed by the federal government, which is the nation’s largest student loan lender.

But as the debt passed through many hands before landing in National Collegiate’s trusts, critical paperwork documenting the loans’ ownership disappeared, according to documents that have surfaced in a little-noticed legal battle involving the trusts in state and federal courts in Delaware and Pennsylvania.

National Collegiate’s legal problems have hinged on its inability to prove it owns the student loans, not on any falsification of documents.