The news comes as the historic business has confirmed that the plant in the city will close on December 20.
The site, based on Bushbury Lane, has been in operation for the last 90 years.
MORE: Homes on way at former Goodyear factory site in Wolverhampton
A total of 330 people worked at the plant when the closure was announced last year, with 96 people still at work there.
Following the announcement of the closure, Goodyear had offered staff the chance to transfer to work in Mexico, but no one took up the offer.
Cyril Barrett, chairman of the Goodyear branch of Unite said: "It was unrealistic for anybody to move to Mexico.
"It would be a total change of culture and lifestyle for people coming from Wolverhampton to go there, so it doesn't surprise me that no one took up the offer.
"People are just really sad. It's like a family breaking up.
"People feel like they've been part of the family at Goodyear for many years, and now that it's coming to an end it's very emotional."
Most of the staff that formerly worked at Goodyear have, however, managed to find new jobs.
Mr Barrett said: "The majority of the 330 members of staff that worked at Goodyear when the closure was first announced have found new jobs.
"Some of the people who were working there were at retirement age though so they have stopped working.
"We've had people take up jobs at places like JLR, and at food companies in Stourbridge and Telford, but it has been quite difficult for people to acclimatise to working somewhere new, especially as some staff have worked at Goodyear for 20, even 30 to 40 years."
Mr Barratt added: "There will be no staff at all at the site from June next year, though the definitive date has not yet been decided."
Last week, £1million was donated to Compton Hospice for their community co-ordination hub.
The money had been raised through donations made by Goodyear workers.
The workers have used their 5/344 Transport and General Workers Sick and Distress Fund, to pay for the forthcoming development of the Wolverhampton-based hospice charity.
The development is expected to be completed in 18 months time and will include a nod to Goodyear with the roof having a tyre-tred design and a metal plaque will be added to the building once it is finished.
In June last year, when the closure was first announced, Goodyear said it was aiming to improve efficiency by transferring the production of commercial retreaded tyres and compound mixing carried out at Wolverhampton to other plants in Europe, the Middle East and Africa.
Management also said at the time that the plant had become commercially uneconomic due to falling sales and the value of the pound on international markets.
Goodyear was first founded back in 1898 in Akron, Ohio, USA.
The company expanded internationally and plans were revealed in 1913 to open a branch in Rio de Janeiro, Brazil.
In July 1927, Goodyear bought the Wolverhampton premises and the first tyres were manufactured in December that year.
The company switched to war production in 1939 where factory employees worked 20 days on and just one day off.
At its peak, the factory employed 7,000 workers.