It is possible to have either a positive or negative net worth. A negative net worth would indicate that an entity has greater liabilities then assets. Net worth typically plays a role in credit ratings.
A net worth can contain stocks or other items (both liabilities and assets) that vary in value with time. This can result in fluctuating net worth without any changes what items appear on a balance sheet.
While a net worth may say that an entity is worth a given amount of money, that does not necessarily mean that they entity has access to that money. The assets include such non-liquid investments as real estate, trust funds, or businesses. If an entity were to attempt to cash out these assets then the received value may be much lower then the listed value. For example if the money were held in a savings bond that matured on a specific date. The net worth may indicate the mature value of that bond, even though it has not matured yet. If the bond were cashed out today then the actual value would be much lower.