In late May, about 35 technology employees at Disney/ABC Television in New York and Burbank, Calif., received jarring news. Managers told them that they would all be laid off, and that during their final weeks they would have to train immigrants brought in by an outsourcing company to do their jobs.

The training began, but after a few days it was suspended with no explanation. In New York, the immigrants suddenly stopped coming to the offices. Then on June 11, managers summoned the Disney employees with different news: Their layoffs had been canceled.

“We were read a precisely worded statement,” said one of the employees, who was relieved but reluctant to be named because he remains at the company. “We were told our jobs were continuing and we should consider it as if nothing had happened until further notice.”

Although the number of layoffs planned was small, the cancellation, which was first reported by Computerworld, a website covering the technology business, set off a hopeful buzz among tech employees in Disney’s empire. It came in the midst of a furor over layoffs in January of 250 tech workers at Walt Disney World in Orlando, Fla. People who lost jobs there said they had to sit with immigrants from India, some on temporary work visas known as H-1B, and teach them to perform their jobs as a condition for receiving severance.