When Carson’s stores ring up their final sales — likely by late summer — they will leave behind a 164-year history as one of Illinois’ iconic homegrown department store chains. They will also leave their landlords with millions of square feet of empty retail space to fill.

Parent company Bon-Ton Stores filed for bankruptcy protection earlier this year. A bankruptcy judge on Wednesday approved the sale of the company’s assets, including Carson’s and other department store chains, to a joint venture of two liquidation firms and a group of company bondholders after the retailer failed to find a bidder willing to keep the business alive.

Going-out-of-business sales began Friday and will last about 10 to 12 weeks. But finding tenants to move into the stores Carson’s will vacate when sales end likely will be a much taller task than finding shoppers to buy its discounted sweaters and slacks.

In Illinois alone, the liquidation of Bon-Ton — which, in addition to Carson’s, owns the Bergner’s chain — could leave vacant nearly 40 stores covering 4.3 million square feet. All that vacant retail space joins the 31 Illinois stores Toys R Us began closing last month — another 1.3 million square feet.

Those numbers aren’t huge compared with the overall retail real estate market. The problem? The 40,000-square-foot big-box stores Toys R Us occupied and the even bigger department stores Carson’s and Bergner’s occupied are out of fashion with many retailers as online shopping has grown.

One indication of shoppers’ changing habits: More than 100 million people now pay for Amazon’s Prime membership, which includes free two-day shipping, among other perks, CEO Jeff Bezos said Wednesday in a letter to shareholders. Even when shoppers stick with traditional retailers, an increasing share of their purchases are made on those retailers’ websites, which means some retailers are finding they simply don’t need as much bricks-and-mortar space.

Successful malls are working to reinvent themselves by filling empty anchor stores with new kinds of tenants, like entertainment and dining options. But when there’s a glut of vacant space, weaker malls can struggle to find new tenants.

“It’s the cumulative effect that’s putting pressure on mall owners,” said Suzanne Mulvee, research director and senior real estate strategist at data firm CoStar Group. “In some, they’ve been able to re-lease them quite easily. In others, it’s forcing some pretty tough decisions.”

One of the Carson’s that will close is an almost brand-new store in south suburban Evergreen Park, built on the site of late Chicago real estate mogul Arthur Rubloff’s Evergreen Plaza. One of the country’s first indoor malls, Evergreen Plaza was recently demolished and redeveloped as an outdoor shopping center. Shoppers lined up for the grand opening of the revamped Carson’s store in September 2016, and the Evergreen Park High School marching band performed.

“All the ladies love Carson’s at Evergreen,” he said.

Still, Sexton said he’s optimistic they’ll be able to find a replacement. The property is otherwise fully leased, and a Burlington discount department store is opening later this month, he said.

“The others stand as their own as great retail,” Sexton said. “I think we’ll fill it in and move on.”

There are signs supporting his optimism. The overall retail vacancy rate in the Chicago metro area has steadily declined since the closure of grocery chain Dominick’s in 2013, and at 6 percent, it is below the area’s historical average, according to CoStar.

But the stores that retailers have been closing nationwide — 32 million square feet so far this year, on top of 100 million last year, according to CoStar — tend to be unpopular oversize stores.

Sears Holdings Corp. shut down 303 Kmart and 123 Sears stores over the course of 2017, and more have followed. Sears recently announced its last store in Chicago — at the Six Corners shopping district on the edge of the Portage Park neighborhood — will close this summer.

Meanwhile, J.C. Penney announced 138 closures last year, and Macy’s is working its way to 100. Since the start of this year, Sam’s Club announced 63 store closures, and Bon-Ton announced 42 shortly before filing for bankruptcy protection in February.

CoStar studied 185 department stores that closed in 2016 and found that only 40 percent of the spaces secured a new tenant in the following year, Mulvee said. About 30 percent managed to find a new tenant that drove similar sales, like a comparable department store, grocery store or a Dick’s Sporting Goods, but 10 percent settled for a lower-quality retailer, she said.

Not all properties are created equal. Some midsize urban stores will be easy to fill, like a “very desirable” Carson’s at Riverside Plaza near Chicago’s Union Station, said Gregory Kirsch, executive managing director at commercial real estate firm Newmark Knight Frank.

Those stores are often split into smaller spaces that can draw fast-casual or full-service restaurants, Kirsch said. Grocery stores have been filling some larger stores, according to CoStar, and expanding retailers could snap some up too. For example, a bankruptcy judge last week approved the sale of a Vernon Hills Toys R Us to the company behind PGA TourSuperstores.

Suburban malls pose a much bigger challenge, Kirsch said. The strongest malls have been turning their empty anchor stores into entirely new businesses or slicing them into smaller spaces.