C172 Flight Instructor reported an NMAC at a non-towered airport.

Narrative

The Cessna 172 was on a training flight (private pilot student with a flight instructor) doing pattern work (takeoffs and landings) at ZZZ. The Cessna 172 had just turned base to final approach on Runway XX - about 2 miles from the runway. The Cessna 172 was descending about 500 feet a minute for landing; when the flight instructor noticed an aircraft wingtip looking down to the left side of the aircraft. The flight instructor veered slightly right and looked down to see a Piper 46-600TP directly underneath about 100-150 feet to the Cessna 172. The Cessna executed an evasive action - full power; veered slightly right and did a go-around approach for Runway XX; keeping the Piper PA-46-600TP in sight the whole time. The Cessna 172 did not have a working ADSB-In.The Cessna 172 made all of the required radio calls in the pattern - cross wind; down wind; base and final. The Piper PA-46-600TP made no calls on the ZZZ unicom frequency.When the Cessna 172 did the go-around for Runway XX; the flight instructor tried to reach the Piper PA-46-600TP numerous times on the ZZZ unicom frequency; with no response.When the Cessna 172 landed; the flight instructor went to the ZZZ FBO office to discuss the incident with the other pilot; but the pilot of the Piper PA-46-600TP had already left. The line crew told the Cessna 172 flight instructor that the pilot of the Piper PA-46-600TP did state that his Collision Alert did alarm that there was traffic within 200 feet; but he said he never saw anyone. The line crew did state that they tried to reach the Piper PA-46-600TP on the ZZZ unicom frequency; but did not receive a response.It appears evident that the Piper PA-46-600 TP was on the wrong frequency the entire time.