Which of the following would indicate that a financial institution is unable to meet its obligations?

The indication that a financial institution is unable to meet its obligations is linked directly to its solvency status. When an institution is described as insolvent, it means that its liabilities exceed its assets, rendering it unable to pay off debt as it comes due. This critical financial condition highlights that the institution lacks the financial resources necessary to meet its commitments, creating an immediate concern regarding its operational viability and stability.

In contrast, if an institution is solvent, this signifies that it has sufficient assets to cover its liabilities. Being profitable means the institution is generating revenue and positive income, which does not necessarily equate to its ability to meet obligations. The term "secure" could imply a strength in its financial positioning, but it does not directly address solvency. Thus, the focus on insolvency accurately reflects a state of financial distress that prevents fulfilling obligations, making it the correct answer.