Can a company end up with negative shareholders' equity, and what does it signify?

• No; a company can post accounting losses, but equity is floored at zero once paid-in capital is fully absorbed
• No; auditors require a fresh equity raise before the balance would ever be allowed to go negative
• Yes, and it always means the firm is insolvent and headed for liquidation, since it can no longer cover what it owes
• Yes, but only at firms carrying heavy debt, because interest costs are what erode the equity balance over time
• Yes; it comes from accumulated losses or large buybacks/dividends, and can signal distress or heavy capital return