The Feb. 26 letter asks Hollywood to "take a small stand for American workers." It asks Oscars attendees to wear on their lapels a pin reading, "Keep the Hugo Boss Plant Open."
Workers United, which represents most of the plant's employees, said the plant is profitable and the company is shutting it because it can make clothing more cheaply in Europe. The clothing company, famed for its stylish fashion, has a facility in Turkey and contract workers in Romania and Bulgaria.
The union, affiliated with the Service Employees International Union, is asking fans to join Glover by signing an online petition urging Hollywood to shun Hugo Boss at the Oscars.
Hugo Boss AG, based in Metzingen, Germany, said the plant is under capacity and isn't globally competitive. It makes two lines of men's suits there.
During union negotiations last year, the company told workers it wanted to lower wages from $13 an hour to $8.30, Ohio union director Dallas Sells said.
In a letter to workers in December, Hugo Boss chief operating officer Andreas Stockert said that the company had negotiated in good faith with the union and that it had a responsibility to shareholders.
It announced the closing in December, stunning employees, most of whom are at the $13-an-hour pay level.
Beyond Cleveland, Hugo Boss employs some 900 people in the U.S. in its stores and showrooms and in administrative positions.