DOVER, Del. — Should a worker who was injured on the job and now can’t find other employment because she is in the country illegally be entitled to continue receiving disability benefits?

That was the question the Delaware Supreme Court weighed on Wednesday in the case of Magdalena Guardado, who injured her left wrist in 2010 while working at Roos Foods, a cheese company that ceased operations in 2014 following a listeria outbreak and suspension of its food facility registration.

After being paid various periods of total disability, Guardado returned to work until undergoing surgery in 2014. A doctor cleared her to return to work less than two months later, and the company subsequently sought to terminate her disability benefits.

The Industrial Accident Board denied the company’s petition last year, saying Guardado, while physically capable of working, was a “displaced worker” because of her immigration status, and that the company’s labor market survey had not shown there were jobs within Guardado’s reach.

“How exactly does an employer go about showing that an illegal alien has job opportunities?” Justice James Vaughn Jr. asked Walt Schmittinger, an attorney for Guardado.

“That’s a difficult proposition. And yet we know that those jobs exist,” Schmittinger said.

Andrew Carmine, an attorney for Roos, argued that the board erred in focusing solely on Guardado’s immigration status and had failed to do a proper displaced worker analysis.

Carmine also argued that a Superior Court judge who upheld the board’s decision earlier this year exceeded his authority because his decision took into account other factors that the board did not consider, including that Guardado is unskilled, has little education and does not speak English.

Justice Vaughn suggested that Roos has found itself in a situation in which it must prove that there are employers who are willing to acknowledge that they will commit an illegal act by hiring someone living in the country illegally.

“How does an employer do that?” he asked.

Chief Justice Leo Strine Jr. said the case presents “important and new issues” for the court, which is expected to rule within 90 days.

Meanwhile, Guardado, who earned $306 a week at Roos, remains entitled to disability benefits of $204 a week.