On May 28, 2016, about 1257 Pacific daylight time, a Cessna 172 airplane, N739ZE, is presumed to have crashed in the Pacific Ocean about 5 miles north of Avalon, California. The airplane was registered to Libra Air Inc. and operated by Encore Flight Academy as a 14 Code of Federal Regulations Part 91 instructional flight. The certified flight instructor and student pilot have not been located and the airplane is missing; presumed to be destroyed. Both pilots are presumed to be fatally injured. Both instrument and visual meteorological conditions prevailed in the area, and no flight plan had been filed. The airplane departed Catalina Airport (AVX), Avalon, California about 1254 and was destined for Van Nuys Airport (VNY), Van Nuys, California. On May 29, 2016, a concerned family member of the student pilot contacted the Los Angeles Sheriff's Department (LASD) to report their family member missing. They reported that the student pilot went flying with an instructor the day prior, and they have not heard from him since. The LASD contacted Encore Flight Academy, who reported that the accident airplane was not at their facility, nor do they have record of it returning the day prior. The NTSB attempted to contact the operator numerous times, but to no avail; nor did the operator submit a Pilot/Operator Aircraft Accident/Incident Report, NTSB Form 6120.1. Review of radar data for the area revealed that the airplane took off from VNY and landed safely at AVX at 1209. At 1254, the airplane took off from AVX with its transponder in the off position and flew north. At 1257 the track ends over the water 5 miles north of AVX. An oil slick consistent with drift models was present in this area. A weather study revealed that at the time of takeoff from VNY, the weather at AVX reported 4 miles visibility, mist, and an overcast ceiling of 300 feet agl. When the airplane arrived at AVX weather indicated 8 miles of visibility and an overcast ceiling of 500 feet agl. Four minutes prior to the airplane departing AVX, weather reported 9 miles of visibility and a broken ceiling at 800 feet agl, however, in the remarks section it reported the ceiling varied between 600 feet agl and 1000 feet agl. In addition, satellite imagery indicated a thick marine layer was just north of AVX, and in the vicinity of the presumed accident location. The U.S. Coast Guard, Civil Air Patrol, and private entities conducted a search for the missing airplane along the apparent route of flight; however, no wreckage was found. The pilots and airplane remain missing.