“It is very frustrating that you can’t share your story with the public,” said one former Abbott manager, who had worked for the company for 13 years, rising to an important supervisory position. He had prepared a 90-page manual for his foreign replacements showing how to perform every detail of his work. With a disabled child who requires medical care, he said he had to take his severance and its nondisparagement clause, since it extended his medical benefits. So he asked to remain anonymous.

“I’ve been laid off before, I can understand that,” he said. “But these visas were meant to fill in gaps for resources that are hard to find. This time the company actually asked me to transfer my knowledge to somebody else. That changes the equation.”

According to federal rules, temporary visas known as H-1Bs are for foreigners with “a body of specialized knowledge” not readily available in the labor market. The visas should be granted only when they will not undercut the wages or “adversely affect the working conditions” of Americans.

But in the past five years, through loopholes in the rules, tens of thousands of American workers have been replaced by foreigners on H-1B and other temporary visas, according to Prof. Hal Salzman, a labor force expert at Rutgers University.