A woman pushes a cart of groceries to her car outside an Albertson's store in Denver, Colorado.

It also spurred a furious grocery war with country's largest retailer, Walmart . The giant, which has 5,000 stores cross the U.S. has been investing heavily in technology and focused on going after higher-income shoppers than its traditional base.

The most notable of those challenges is Amazon's acquisition of Whole Foods, which gives Amazon a brick-and-mortar distribution network and brand name it can combine with its powerful Amazon Prime membership program.

Cerberus and a consortium of investors formed Albertsons in 2006 and merged it with Safeway in 2015. But the grocery industry has gotten significantly more difficult over the past decade, and Albertsons now finds itself confronted with fortified competitors and hampered with $12 billion in debt.

The scuttled deal is just the latest in a string of disappointments for Cerberus, which has unsuccessfully tried to shed Albertsons multiple times. Those efforts include an IPO it abandoned at the last minute in 2015 as well as attempts to combine with both Sprouts Farmer Market and Whole Foods Market last year.

Albertsons Cos last night called off its merger with Rite Aid that would have provided its private equity owners, Cerberus Capital Management, a long-awaited means to unload its more than decade-old grocery investment.

"They [Walmart] are in the 800-pound guy in our industry," Albertsons Chief Operating Officer Jim Donald recently acknowledged to CNBC in an interview.

Meantime, both giants are shifting the demographic focus, with Walmart going after higher-income shoppers than traditional, and Amazon going after lower-income. That means Albertsons is getting squeezed from both ends.

To keep pace with its competitors, Albertsons would likely like need to go public to pay down its debt. But there, it faces a dual-edged sword. In its first IPO attempt in 2015, it pitched to investors unrealized savings from the Safeway merger and further acquisitions across the still fragmented grocery industry. That pitch is no longer consistent with how the industry is thinking about growth.

Retailers are now focusing away from broadening their footprint to investing in technology and capabilities. That shift is in part why Supervalu had a difficult time unloading its retail businesses, people familiar with the matter have told CNBC, opting instead to sell its whole business to food distributor United Natural Foods. UNFI has said it plans to divest its retail business, includes banners like Cub Foods and Shoppers in a "thoughtful and economic manner."

That shift in focus is highlighted more clearly by Kroger, Albertsons' public and better capitalized competitor, which has spent the year building its digital business while scaling back its non-grocery business.

New competition from the likes of Amazon "challenge traditional business models and have pushed traditional players such as Walmart and Kroger to invest in online/home delivery businesses," investor advisory service ISS recently wrote. Albertsons' debt places it "at a disadvantage in the challenging environment."

The Cincinnati-based grocery chain, whose digital efforts are led by Chief Digital Officer Yael Cosset, has taken a stake in British online supermarket Ocado, acquired meal kit company Home Chef and launched a grocery delivery service called Kroger Ship.

In the interim, it has also announced the $2.15 billion sale of its convenience store business and potential sale of its Turkey Hill ice cream brand to fortify its resources.

To be sure, Albertsons had made some headway in its own digital business, acquiring meal kit company Plated and expanding its partnership with delivery service Instacart. But those efforts have been distracted by the efforts to integrate Rite Aid over the past few months and are limited by Albertson's own capital constraints.

Meantime, Kroger's performance has consistently surpassed Albertsons, noted advisory firm Glass Lewis

"In light of Albertsons lower sales growth and profit margins relative to Kroger and other peers, which place Albertsons in the lower quartile among peers on those metrics," Glass Lewis recently wrote.

The question now — with its debt load and emboldened competitors — whether it can sufficiently improve on its own.