The seven remaining stores in the group will reopen while the appointed receiver Neil Hughes, of Hughes Blake, seeks a buyer.
Balke declined to say how much is owed by the Byrne group, but indicated that he is open to offers for the seven shops: "The hope would be that everything will be done to keep as many of the stores as possible trading.
"It is too early to say what the prospects might be. The hope is to save the majority of the jobs but there are no guarantees."
Byrne’s World of Wonder formerly operated 21 stores with 350 staff and in 2006 had a turnover of €50 million. The retailer closed its two Dublin stores, at Coolock and Liffey Valley, in 2009, followed by seven more stores in February 2010 and has continued to close stores since.
Byrne’s World of Wonder issued a statement yesterday, which said: "Like all retailers, we have been operating in an environment of collapsing consumer demand and despite every effort, we have been unable to overcome this challenge.
"We would like to thank all of our employees for their hard work and dedication over the past 35 years and also our suppliers and our customers."
The Byrne family business is based in Enniscorthy, Co Wexford, where three of its stores are located. The other four are in Wexford town, Gorey, Carlow and Kilkenny.