Total Stockholders’ Equity is almost always a positive number, but it is possible for it to be negative. This typically occurs when the company incurs significant losses, which results in a large Accumulated Deficit. However, accumulated other comprehensive losses (past losses that bypassed the Income Statement) and treasury stock (shares the company repurchased) can also reduce Stockholders’ Equity and contribute to it being negative.
When Total Stockholders’ Equity is negative, it is referred to as Total Deficit. Negative equity typically precedes a bankruptcy (since the company is probably losing a lot of money) but it does not mean the shareholders owe the company money.