According to the flight instructor, after conducting a practice instrument approach and a subsequent touch-and-go landing in the single-engine airplane, they executed the published missed approach procedure which included holding at a fix located about six miles offshore. Shortly after establishing the airplane in the hold the engine began to vibrate. In an effort to correct for the vibration, the flight instructor moved the mixture to the full rich position, but the engine vibration increased followed by a loud bang. A check of the multi-function display’s engine page revealed no exhaust gas temperature on the number 2-cylinder and a complete loss of oil pressure. The flight instructor then disengaged the autopilot and turned the airplane toward the shoreline. A “MAYDAY” call was transmitted to air traffic control (ATC) as the cockpit began to fill with smoke and oil became evident on the engine cowling. The fresh air window vents were opened in an effort to vacate the cockpit of smoke and ATC provided vectors to a nearby airport. During the emergency descent, while attempting to maintain best glide speed, they tried to restart the engine to no avail, and subsequently secured the airplane, donned their life preservers, and opened the airplane’s cockpit canopy. The flight instructor ditched the airplane in the ocean waters. During the ditching the empennage separated from the fuselage resulting in substantial damage. The airplane sank in the ocean waters and was not recovered or examined after the accident; therefore, the reason for the loss of engine power could not be determined.