Overview
Because of the large variation of types of structured securities, it is generally not possible to trade a strcutured security at an exchange or otherwise public market. (there are exceptions) This typically means that structured securities have to be traded over the counter (OTC).
This does not mean that once a security is purchased, the owner then must keep the security to maturity. A company can actively trade a security, but this is done with a dealer of some sort. (typically an investment bank)