When his cryptocurrency exchange started teetering in early November, Sam Bankman-Fried went on Twitter to calm everyone down. FTX was fine, he insisted. Nothing to worry about. Joining him in the outreach was a close colleague: Caroline Ellison, the 28-year-old chief executive of Alameda Research, a crypto trading firm Mr. Bankman-Fried also founded.

Ms. Ellison claimed repeatedly that Mr. Bankman-Fried’s empire was on stable financial footing. On Twitter, she sparred with Changpeng Zhao, the chief executive of Binance, who was voicing doubts about FTX and Alameda.

But her words weren’t enough to keep FTX alive. A run on deposits, website prompted partly by Mr. Zhao’s comments, left the company owing $8 billion. Within less than a week, FTX and Alameda had filed for bankruptcy. Now the companies are facing investigations by the Justice Department and the Securities and Exchange Commission, focused on whether FTX’s shortfall arose because it had illegally lent its customers’ deposits to Alameda.