Flight Instructor with student reported while on an ILS approach the glide slope ground equipment failed resulting in no glide slope indication and aircraft flight toward terrain event. Flight crew corrected altitude and continued to landing.

Narrative

I was on a training flight with my instrument student. We were on an IFR flight plan going to ZZZ. We were being vectored to final for ILS RWY XX. As we were being vectored I checked the PFD (Primary Flight Display) and noticed the glideslope had not come alive. I did not think anything of it; at the time; because we were not established inbound. Once we were established inbound I had to communicate the radio call because my student was busy. We were instructed to maintain 2;700' until established clear ILS RWY XX. Once established my student began descending and the approach was smooth and stable. As we were approaching minimums; I noticed we were getting uncomfortably low a little too far from the runway. This is when I looked over at the PFD and noticed there was no glideslope and I instructed my student to take her foggles off and add power. After we landed; we debriefed the event and I informed her that if the glideslope does not come in then she should use the LOC mins. I also talked to her about going around. After we landed I double checked NOTAMs and there was nothing for the glideslope as when we checked during our preflight. After we got fuel and were gathering information to leave; my student and I noticed on the ATIS that they were reporting the glideslope for ILS XX to be unusable. For a second; I was thinking; 'how did we miss that'. However; during our departure an airplane requested the ILS XX and ATC advised them the glideslope was not working and asked for another approach request. When my student and I requested the ILS they did not do this; leading me to believe it failed around the time we shot our approach. This then made me realize that we did not notify ATC of the glideslope failure. Throughout my training; I have been told about this scenario and instructed what to do; but I have never actually had it happen. After this realization I then told my student we should have told ATC about the glideslope failure.