Flight Instructor reported a NMAC during landing phase. Flight landed without incident.

Narrative

During final approach I noticed the plane that was cleared to land behind us turned their base early. Assuming that ATC was going to correct the situation I pointed it out to my student and told him to keep us below that plane since we were cleared first. ATC did not see the situation unfolding as they seemed to be distracted by radio calls from another plane. I did not feel safe to pull any evasive action as we were close to the ground at night with limited space. I watched as Aircraft Y went over our wing as he turned onto final on top of us. When ATC was finished with their calls to the other plane I quickly confirmed our landing on XXL to get the controller's attention to what was happening on final approach. They told Aircraft Y to make a left 360 to rejoin final but the first call was missed by the plane. They were able to get it on the second call from tower and made their left turn narrowly avoiding a midair collision and loss of life.This situation should have been corrected firstly by the pilot of Aircraft Y. When pilots are cleared to land behind traffic they should be getting that traffic in sight before turning base or ask ATC if unsure. Tower should have been paying closer attention to planes that are in the air over planes that are on the ground. Not sure why the controller never checked final approach after clearing two planes to land. I feel that they have a responsibility to double check planes that are on final and that there is no collision courses with other planes. The only real evasive action that I could have taken here would have been to climb which I felt would have made things more unsafe by putting us directly into Aircraft Y flight path. Planes that are on final approach shouldn't have to be pulling crazy evasive maneuvers and think ATC needs to do a better job of watching pilots after clearing them to land behind somebody.