Its remaining site with 56 disabled workers recycling computers at Porth, Rhondda, is on the verge of being sold to its managers.
The Department of Works and Pensions (DWP) said it had “worked extensively” with potential buyers for Baglan but there were no viable bids.
Seven Remploy factories in Wales were closed by the UK government last year because they were deemed “unviable”, putting 280 people out of work.
There are currently 13 Remploy factories left throughout the UK.
The closure of three of those – Baglan, Blackburn and Sheffield – was announced on Wednesday as the company said it had failed to find a buyer for its furniture business.
All workers are at risk of compulsory redundancy, although they will be invited to consultation meetings over the next 30 days.
The union Unite called the decision a “shameful act”.
“The workforce has been kept in the dark and face a future of fear and insecurity as this cruel government consigns them to a life on the dole,” said general secretary, Len McCluskey.
TUC general secretary Frances O’Grady also said the imminent closures had “potentially devastating consequences”.
“There are already far more jobseekers than vacancies in these areas so their chances of finding new jobs are slim, particularly as many employers remain reluctant to hire severely disabled people,” she said.
Remploy said the remaining factories were in the process of being transferred to new ownership, including Porth.
A spokesman said: “Porth is part of our E-cycle business and is in the process of being sold to a new company E-Cycle Ltd which has been set up by two Remploy managers.
“It is anticipated that the sale will be completed by the end of next week.”
The demise of the last Remploy factories in Wales marks the end of an era which began in 1946 when the company opened its first factory in Bridgend employing disabled ex-miners to make furniture and violins.
However, a Remploy spokesman said that while its manufacturing operations across the UK will end, its recruitment arm will continue, where it places disabled workers into mainstream employment.
In Wales, Remploy will continue to have branches in Bridgend, Cardiff, Newport, Swansea and Wrexham.
A DWP spokesman said: “Our priority throughout this process has been to safeguard jobs for disabled people, which is why we offered a wage subsidy of up to £6,400 per disabled employee to encourage interested parties to come forward.
“All disabled employees at the three factories affected will now be guaranteed tailored support from an £8 million package, including a personal case worker to help with the transition to mainstream employment.”