As Bangladesh mourns the death of more than 100 workers killed in a factory fire over the weekend, attention is turning to the labels found among the charred debris and what role they could have played in preventing the worst industrial disaster in the country's history.

The factory, owned by Tazreen Fashions, produced clothing for U.S. supermarket giant Wal-Mart, European clothing retailer C&A and produced garments for several other companies, including Hong Kong sourcing firm Li & Fung.

It is just one of about 4,500 apparel factories in Bangladesh that employ an estimated 3.4 million workers, usually young women who work long hours dying, cutting and stitching for a minimum wage of approximately $43 a month.

Campaigners say that workers' safety is being put at risk by the complex and fragmented nature of global supply chains used by many of the world's top clothing brands, which largely rely on cheap labor to turn a profit.

In some cases, companies are unsure which factories are producing the clothing that ends up in their stores, making it impossible for a brand to know whether safety standards are being met.

And workers' rights groups say factory bosses in places like Bangladesh often have little incentive to improve working conditions when contracts are short and orders not always renewed.

"You have this dilemma where the factory doesn't have the funds to improve the factory or there is no faithful relationship (with the supplier)," Judy Gearhart, executive director of the International Rights Labor Forum told CNN.

"They don't know if they are going to have the order from Wal-Mart three years down the road. They don't know if they are going to be able to make the investment.

"It's really the whole problem we have with global supply chains. The global brands have taken a distance from the responsibility of the workers that actually make the product."

Wal-Mart said in a statement to CNN that a supplier had subcontracted work to Tazreen "without authorization and in direct violation of our policies." It added that it had ended its relationship with that supplier and would "continue to work across the apparel industry to improve safety education and training in Bangladesh."

C&A said it had placed an order for 220,000 sweaters, its first commission with Tazreen, and has sent a representative to Bangladesh to see how the company can help the victims.

Li & Fung, which used the factory to make clothes for other brands, has offered $1,200 in compensation to each family of every victim.

But fires like the one at Tazreen are all too commonplace, campaign groups say.

According to Sanjiv Pandita, executive director at the Asia Monitor Resource Centre, more than 500 garment workers have died due to factory fires since 2006. Emergency exits are few in number and those often blocked by work in progress and poorly signposted.

The Bangladeshi government has ordered the police, fire service and civil defense authorities to begin investigations into the cause of the fire and the deaths.

In the meantime, Minister for Labor and Employment Rajiuddin Ahmed Raju said that his ministry had ordered the closure of clothing factories which do not have more than one emergency exit.

"I'll sit with the senior officials of the ministry tomorrow (Wednesday) and form a committee to identify the factories which do not have an adequate number of emergency exits," he told CNN.

"We've seen many factories have storage of fabrics or other things blocking the emergency exits. We've asked the factory authorities to remove all those (items) immediately," Raju said.

It's a problem that goes beyond Bangladesh. Despite decades of campaigning by labor groups and tighter legislation, factories across Asia have proved to be deathtraps for their workers.

A fire at a garment factory in Karachi in October killed almost 300 workers, making it the worst factory disaster in Asia since a Thai blaze killed 188 toy factory hands in 1993.