TOKYO—Toshiba Corp.’s problems threatened to spiral out of control as the electronics giant projected a $6.3 billion write-down, postponed its earnings report because of allegations of impropriety and said its chairman was resigning—all in the space of a day.

The delay in the earnings report sent Toshiba shares down 8% in Tokyo trading Tuesday, and its president said he was willing to sell most or all of Toshiba’s profitable flash-memory business to help the company survive past the March 31 end of its fiscal year.

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