Monsters don't stop chasing the player (and the fight music doesn't end) until the player or the monster is dead.
Openmw 0.35.
I slept in the wilderness and was interrupted by a monster I couldn't find, presumably because it had spawned in some rocks or something. No matter how far away I got, the fight music just would not stop. And since I couldn't kill whatever attacked me, I had to load from an earlier save to get rid of the inappropriate music.
To test this I hit a mudcrab in Seyda Neen and ran away. The fight music played no matter how far away from the creature I got. It stopped once I entered a new cell, then when I walked BACK into Seyda Neen, the fight music started up again.
Originally I had a few mods running, but I tested this in a clean version with nothing but morrowind.esm running and the behavior still occurred.
(RM-2567 from redmine: created on 2015-05-18 by Brendan Jones, , closed on 2017-08-28 by nobody, duplicates #3476)