PA-28 Flight Instructor reported an engine failure on final approach during a training flight after the student switched fuel tanks. The instructor took control; switched fuel tanks; which restarted the engine; then landed safely on the runway.

Narrative

I was teaching a pre-solo student how to land at various airports near ZZZ. On our way back from those landings into ZZZ we were doing our last landing for the flight; our engine started sputtering on short final for Runway XXR. I started troubleshooting immediately; once the engine completely cut off I immediately [requested priority]. I aimed towards Runway XYL and requested landing there. I completed the engine out flow procedure; and switched my fuel tanks during that procedure flow and the engine started up again. We were at roughly 500 ft AGL when the engine got back on and I proceeded to land on XYL. The firetrucks were rolled out and I explained that the issue was fuel exhaustion and we were able to fix the issue. I understand that I was the PIC for this flight and I showcased a dangerous level of complacency. I was not watching my student switch the fuel tanks and I have most certainly learned from this. I understand complacency is a major factor when it comes to pilots and it exhibits the hazardous attitudes. This will not happen again; I have much more stringent checklist in place with timers as well. I have completed extra training with my company and I am thankful for the help of the ATC team at ZZZ. There is no excuse for what happened and I assume all responsibility for this. I vow for this mistake to not happen again and I will definitely verify my student while also verifying if I am exhibiting any hazardous attitudes; along with staying true to my training and certification process by following checklist accordingly.