Small Aircraft Pilot on short final reported a NMAC with an aircraft experiencing engine trouble that flew 200 ft. below them on approach to the parallel runway. Tower issued traffic and advised the reporter to stop their descent.

Narrative

I was flying the ILSXXL approach at ZZZ. I had been cleared to land by the Tower and was on a 3 mile final; following the glide path for a stabilized approach and landing. At 2200 ft. MSL the Tower notified me that there was an Aircraft X to my nine o'clock 200 ft. below me; and they instructed me to stop descending and level off. Initially; I was unable to find the aircraft for visual separation confirmation; finally I was able to spot them just before they passed under me. The Tower asked Aircraft X why they hadn't followed the last instructions they had been given; which was to fly north; I assume for sequencing. Aircraft X responded that they were having some sort of engine trouble. They mumbled something about pistons.At this point; the Tower [requested priority handling] on behalf of Aircraft X and cleared them for a straight in XXR. This was either when they were flying right under me or just after. I maintained 2200 ft. and then realized I was too high to resume a stabilized approach / final for XXL. I notified the Tower that I was too high. They asked me if I wanted to cancel my flight plan. I responded in the affirmative and squawked VFR. I was then given a left downwind for XXL; which was easy to execute given that I was basically at pattern altitude. I was cleared to land and did so without incident. Traffic coming at me from the left after I had been cleared to land was a surprise. From this experience; I realize the importance and need of continuing to be vigilant in monitoring surrounding traffic even after being cleared to land by the Tower.