Even if the country's unemployment rate went down to 5.5 per cent for May, some Australian workers may not feel secured in their jobs as companies continue to close or put in place cost-cutting measures that may result in some workers losing their means of livelihood.

Among the local workers who will surely join the ranks of the unemployed are about 100 employees of fashion label Lisa Ho which is closing down. The high-end clothes designer was placed under voluntary administration on May 8.

However, on Tuesday, administrator Todd Gammel of HLB Mann Judd, announced it will close three Lisa Ho stores in Sydney, Brisbane and Melbourne by the end of June to give the retailer time to sell current stock.

On the same day, the administrator shuttered six other stores as the company's debt rose to $11 million.

The move would affect the store's spring collection ready to be ordered but had to be cancelled. Ms Ho was upset by the administrator's decision, but Mr Gammel said the designer understood what is happening as she is moving forward as best as she can.

Department store chain Myer and several private equity groups and trade buyers are interested in purchasing the brand. Mr Gammel disclosed that after a Thursday meeting with creditors, there was an offer but the deal fell apart on Friday.

Other Australian fashion brands such as sass & bide, Bettina Liano, Brave, Ksubi, Charlie Brown and Danny Avidan Jayson Brunsdon, but they have survived voluntary administration. Myer purchased sass & bide, Brave and Trent Nathan, and these brands are now flourishing under Myer.

Meanwhile, car maker Holden informed members of the Manufacturing Workers Union in a meeting on Tuesday afternoon that the company needs to cut cost. Holden had initially asked employees to take a pay reduction, but the union disagreed.

Holden is losing $40 million a year in its Australian operations. It has 2,000 workers at its factory in Adelaide.