By Jacky Wong

Activists investors have failed to push for board changes at 145-year old Toshiba. But other welcome developments waiting in the wings could still result in a more attractive, slimmed down company.

Singapore-based activist fund Effissimo Capital Management, Toshiba's largest shareholder with a 10% stake, narrowly failed last month to install three directors on the Japanese company's board. That is certainly a setback for corporate-governance reforms at the storied company, which has been mired in accounting scandals and financial troubles over the past decade.

But there are signs that Toshiba is slowly climbing out from the mess it created three years ago, when cost overruns at its U.S. nuclear unit Westinghouse Electric led to a $6.3 billion write-down and a brush with delisting. Toshiba survived the crisis after it received $5.3 billion from dozens of hedge funds and sold a majority stake in its memory-chip business. Its stock, however, was kicked out of major indexes Nikkei 225 and Topix after it was demoted to the second section of the Tokyo Stock Exchange.

Toshiba could soon return to the top club of Japanese companies. It applied to rejoin the first section of the TSE in April after the exchange relaxed its rules earlier this year. Last month, Jefferies estimated that Toshiba has a 95% chance of rejoining the first section. That means its stock could be included in major indexes and hence attract inflows from passive funds. Travis Lundy, an independent analyst who publishes on investment-research platform Smartkarma, said a Topix inclusion could lead to buying of 60 million to 67 million shares--around 13% to 15% of total shares outstanding--from Japan's passive investors.

A potential initial public offering of Kioxia, formerly called Toshiba Memory, could give the stock another boost. Toshiba, which invented flash memory in 1984, previously said it had no strategic intention to remain in the memory business and intended to return a majority portion of net proceeds to shareholders in principle. Investment banks have sent research reports on the unlisted company to investors recently, a sign that an IPO could soon be coming. The memory market has bounced back after Kioxia dipped into losses last year, so it could be a good time for a deal.

Toshiba owns a 40% stake in Kioxia after a nearly $18 billion deal in 2018 to sell the chip unit to a consortium led by Bain Capital. At two times last fiscal year's sales, its Kioxia stake could be valued at Yen800 billion ($7.49 billion), compared with Toshiba's market value of Yen1.6 trillion. Jefferies estimated Toshiba could buy back Yen300 billion to Yen400 billion of its shares if it sells half of its stake in Kioxia.

In the past few years, Toshiba has exited many unprofitable businesses, including liquefied natural gas and laptops. Selling its memory business will result in a much smaller and less exciting company that focuses on infrastructure services including energy and sewage systems.

But investors who have gone through Toshiba's roller-coaster ride in the past decade may prefer the calmer new look.

Write to Jacky Wong at JACKY.WONG@wsj.com