PA28 Flight Instructor reported observing converging traffic executing a descent into them; resulted in a NMAC.

Narrative

During a training flight with a student pilot we departed ZZZ1 to our local training area called 'southeast practice area'. This area is a stretch of area just south of our departure airport of ZZZ1. The student and myself had just conducted turns around a point at about 2;300 ft. MSL just east of the a Mountain by a known reference point in our local training practice area. I had the student I was training climb to 3;000 MSL and head east bound towards ZZZ airport. While we were en route to ZZZ the student began to grab weather and brief an approach into the destination airport. As we were on the west side of the town depicted on the sectional we noticed an aircraft south of the town heading northbound at 3;500 ft. MSL. I got eyes on this aircraft/traffic and assured my student got eyes on them as well. On first identification of the traffic they were approximately 4 miles away to us and 500 ft. above; however they were heading north and would eventually cross our flight paths. As my student continued to fly the airplane I maintained visual contact with this traffic to ensure proper separation and see and avoid traffic. As we continued to move east the traffic continues to move north. The aircraft by the tail number of Aircraft Y then soon began a sharp descent out of 3;500 MSL to around 3;000 MSL while less than a mile away from us and on an crossing course of us. I quickly took flight controls from my student and banked the aircraft to the (left) to the north in an immediate reaction to their aircraft. I quickly made a frantic call on the practice area frequency to the Aircraft Y wondering why they were establishing a descent into us. As we banked hard to our left (north) and began a descent the aircraft became blocked of our vision by the wing. I continued to change our course until Aircraft Y barely passed behind us at the approximately the same alt. After we evaded the traffic I made a call to the local area and trying to understand why the traffic had established a descent. A reply was made that they were reporting to the local FSDO. At that point I agreed but continued to ask and try to grasp why this aircraft had made this maneuver and descent and I was given no response.