Which type of security can be irredeemable and may be secured or unsecured?

The correct choice is bond. In the realm of finance, bonds are a type of debt security that can be categorized into redeemable and irredeemable bonds. An irredeemable bond, also known as a perpetuity, does not have a maturity date and pays interest to the holder indefinitely. Furthermore, bonds can be classified as secured or unsecured. Secured bonds are backed by specific assets as collateral, while unsecured bonds, also known as debentures, rely solely on the issuer's creditworthiness for repayment.

In contrast, common stock represents ownership in a corporation and does not have a repayment structure like bonds; it can also be affected by dividends based on company performance rather than fixed interest payments. Preferred stock is similar to bonds in that it often provides fixed dividends and may have features of both debt and equity but typically has a set redemption date and does not constitute a perpetual liability. T-bills, or Treasury bills, are short-term government securities that are redeemable at maturity and do not have the characteristics of being either irredeemable or typically secured. This context highlights why bonds are the right answer, as they can indeed be classified as irredeemable and can be either secured or unsecured.