C172 Flight Instructor pilot reported a near collision on the runway when an aircraft landed gear up behind the instructor while still on the runway.

Narrative

I was conducting a flight with a student at ZZZ when Aircraft Y conducted an unsafe pattern entry and runway incursion with a potential collision on the runway.Myself and a student (in a Cessna 172) were coming back from from a training flight north west of the airport when we made an over field entry into the down wind while announcing intentions on CTAF. As we established on the downwind for XX we heard Aircraft Y saying they were 3 miles to the west to also joining the pattern. As I started my base turn we heard another aircraft on a 6 mile final wanting to land XX and heard Aircraft Y make comments about how he was going to do a short approach and they need to break off their approach. As my student turned final I saw Aircraft Y flying overhead still gear up announcing they are base to final #2 while I was #2 behind another landing cessna. I had my concern aware over CTAF and continued our approach. As we landed on the 1000 footers a few seconds later we heard someone on CTAF say 'hey your gear is still up' and a second after that I got a traffic advisory of someone behind me and approaching. I took controls from my student and steered us to the right side of the runway. As I gave controls back I looked behind us and saw Aircraft Y gear up sliding to a stop just past the 1000 footers. At this point we were just passing taxiway 1 slowing to clear at taxiway 2. The 1000 footers to taxiway 1 is approx. 800 feet.I am extremely concerned that if Aircraft Y did not gear up land and rather landed normal that there would have been a collision on the runway. I am also concerned that a 135 operator shows a blatant disregard for safety while attempting to land while another aircraft is on the runway.I feels as if I made the correct choice as to take controls and attempt to move off the runway as quickly and safely as practical to resolve our TA but if we did not have that system in our aircraft I would have completely been unaware.This incident bothers me due to the fact where I do not see what else myself or my student could have done to not put ourselves in that situation.