Mandating a financial penalty if a contract is broken, as in Vidal’s case, has a long history in contract law, but it is relatively new in employment contracts. In the early 1970s, the U.S. Court of Appeals for the First Circuit noted that companies providing “specialized training” to their employees could require reimbursement “if the employee should quit before the employer achieves any benefit.” But the court emphasized that the penalty should be closely tied to the cost of the training. “The employer may not require its ex-employee to make payments to it unrelated to the employer’s damage,” the judges wrote, “simply as a penalty to discourage or punish a job change.”

Seligman told me that when he saw his firm’s first case of stay-or-pay in about 2016, it was the concept of “worker as debtor” that he found “remarkably concerning.” Vidal’s case was unusual because it was an unspecified fee for quitting rather than a fixed amount tied to training costs. A typical stay-or-pay clause is called a training-repayment-agreement provision (TRAP), which stipulates that the cost of on-the-job training will be borne by the employee. If a company pays for a transferable credential, like an M.B.A. or a master’s degree in computer programming, it might make sense to require the employee to stay for a set amount of time. But too often the training is little more than orientation and provides no transferable credentials, according to many workers I talked to in the course of reporting this article.

Though it’s hard to trace the spread of TRAPs, a 2022 letter from the National Employment Law Project points the finger at private-equity firms. Private-equity firms not only tend to replicate contract terms across their suite of businesses, but they have increasingly purchased companies that provide employee training, giving them an added incentive to use TRAPs.

“Not a month goes by that I don’t hear about a new industry that is using TRAPs,” says Jonathan Harris, a law professor at Loyola Marymount in Los Angeles, who studies these agreements. Nevertheless, Harris says, it’s hard to know how many workers are subject to these contracts, because employment contracts are often private. Based on his research, Harris believes it is safe to assume that in every industry in which there has been litigation involving one worker, stay-or-pay clauses are present in the contracts of thousands of others, because of the way businesses tend to copy one another. Hospitals with no relationship to one another have used nearly verbatim language in their contracts, according to Harris, and it’s easy enough to find, say, a blog for owners of roofing companies with advice on how to implement TRAPs. Because stay-or-pay clauses are so common in industries that employ about a third of the entire American work force — health care, transportation and technology — Harris estimates that millions of people might be subject to them.

Kate Fredericks, a 38-year-old pilot from Massachusetts, knows the issues with TRAPs well. After years working as a teacher, she decided to switch careers and follow her father into the airline business. In early 2020, she secured an offer to be a passenger pilot, but the pandemic grounded air travel and her offer evaporated. She had to wait tables for a while but eventually got an offer with Ameriflight, a Texas-based cargo carrier. Ameriflight is a cargo feeder airline; while U.P.S. and FedEx have routes around the country, they still rely on smaller carriers to fly the connecting routes from, say, Lansing to Detroit. The pilots for the feeder airlines are the unseen backbone of the package-delivery supply chain, often flying decommissioned passenger planes on contract. Fredericks moved to Puerto Rico and took a job with Ameriflight. She signed a contract that required her to pay back $20,000 in training if she left within 18 months, training that Ameriflight is required by law to provide in order to stay in operation. Many carriers do not charge pilots for this training. Fredericks thought the pandemic would last at least three years, so it probably wouldn’t matter. She signed.