PA28 pilot reported engine failure on short final and continued to a successful landing.

Narrative

I was returning from ZZZ1 after doing some pattern work with a fellow pilot when we experienced a loud banging noise coming from the engine. He was flying at the time; but I was PIC. I took the controls and informed him that it was my aircraft. The aircraft started shaking pretty bad and we experienced a partial power loss. The oil pressure and oil temperature were still in the green; but the RPM had dropped from approximately 2400 in cruise to around 1800. We double checked that our mixture setting was appropriate; that the electric boost pump was on and changed fuel tanks. We briefly debated making a right turn and landing on a road. But; the engine was making enough power that we were not really descending or losing too much airspeed so we decided to continue along our path since there was not many structures or houses in between us and the field. The other pilot made a radio call to the tower to inform them of our situation and that we were inbound; but maybe 30 seconds after that we lost even more power. I can't recall exactly what the RPM was; but it was enough that the airplane started to descend and while I had the other pilot making radio calls; I was busy maintaining aircraft control and picking a new place to land. At that point; we were unsure if we would make the runway and it wasn't looking like it was going to be possible. The other pilot informed the tower we would be landing on a road south of the airport. The tower asked us which road exactly. While the tower was asking that; for some reason; the engine ran smooth for about a second and a half and produced power again. That was enough that I decided to continue the left turn towards the airport and had the other pilot inform them that we would be landing on XX left. The tower cleared us to land XX left. We managed to maintain enough altitude along the way that we had a little to spare so though I was concerned we may lose the engine when I reduced the power; I had determined we had enough altitude to make it should that happen. On short final somewhere between the end of the runway and may be a quarter mile or slightly more I reduced power and the engine quit. The prop came to a stop horizontally with a thud. Thankfully; we had maintained enough altitude and air speed to make a power off landing without incident. We were able to continue off the runway and across a taxi away into the non-movement area before stopping. We were then greeted by airport operations staff. I don't think we violated any regulations; but I figure this would be something I should write a safety report about. The rear cylinder on the right hand side of the engine had lost all of the cylinder bolts on the bottom. The forward top two were sheared; but still connected by safety wire. It appears the aft two top bolts were the only thing that kept the cylinder attached to the engine.