As kkards said, it's a restructuring, not a liquidation. So they will continue to operate while the bankruptcy proceeds. They have filed a plan to get relief from some debt, get out of the leases on the stores they want to close, and move forward as a smaller company. It looks like the number of stores they plan to close is less than 10% of the total. Once they emerge from bankruptcy they will continue to operate as a smaller business. Hopefully, they will be left with enough operating cash to be able to provide the products and service their customers have come to expect, though in fewer locations.
Yes, brick and mortar retail sales are down, but the bigger problem for Payless and some of the others is that they were purchased by a group of private equity firms, which used to be called by the more descriptive name of "leveraged buyout" firms, who loaded the company with debt to cover most of the price the firms paid to buy the retailer from its precious owner. But if the business hits a rough patch, like virtually all B&M retailers have recently, the whole thing collapses and they have to file for bankruptcy protection.
This is happening all over retail. Neiman Marcus is on the block for sale, too, and the speculation is that if Hudson's Bay doesn't buy them, they'll be filing for bankruptcy protection, too.