It was a $2 billion investment by SoftBank in January that set the We Company’s valuation at a staggering $47 billion. The public offering could value the company at as little as $15 billion, people familiar with the matter said.

WeWork’s travails will be the biggest public test yet of Mr. Son’s freewheeling and distinctive approach to investing. Since unveiling the Vision Fund in 2017, he has spent money on a dizzying array of businesses, including Uber, a start-up that runs large-scale simulations and a dog-walking app.

Mr. Son has been known to invest hundreds of millions of dollars in start-ups with nascent, unproven business models as long as he thinks they can become giant businesses capable of reshaping the future.

SoftBank and WeWork formally established a relationship in late 2016 during a meeting between Mr. Son and Mr. Neumann that lasted less than half an hour. On a single sheet of paper, the two men sketched out the outlines of what became a $4.4 billion investment. (The deal was announced in August 2017, after months of subsequent negotiations and due diligence.)

Executives within SoftBank have been split over the last two years about how much money the company should invest in the We Company, people familiar with those deliberations have said. Over the past week, the We Company and SoftBank have discussed whether the Japanese investor should put more money into the company to help with the offering, according to people with knowledge of those talks.

Mr. Son was hardly alone in thinking highly of WeWork. Bankers at Goldman Sachs, one of the lead underwriters for the offering, told executives at the company in the spring that their shares could be worth as much as $65 billion.

But in meetings and phone calls over the past several days, the company’s bankers told Mr. Neumann and his team that investors were not prepared to buy into the stock sale at anywhere close to those lofty numbers. They also urged Mr. Neumann to give up some of his control over his business, which stood out even in an age when hot technology companies like Facebook and Lyft regularly granted their founders sweeping control.