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One can make this number negative by paying out quite a bit of equity (e.g. special dividend) or buying back a bunch of shares. The times I have seen it has been the latter (take on debt to buy back a lot of shares).

Your explanation is quite good. One small point: a corporation can't pay out a dividend that exceeds the amount in retained earnings. If the corporation has any subsidiaries, any of the subsidiary retained earnings that haven't been distributed to the parent are restricted from dividends.

The most common cause of a negative shareholders' equity is substantial losses that result in a large negative retained earnings balance.

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