Just look at the HRI List published here every week. You see a lot of deceased horses that have finished their last race not too long ago, but appear 3-4 weeks later on this very same list.
In-running comments like: Took keen hold, in rear, headway after 4f, lost position halfway, weakened over 3f out (jockey said mare ran keen early on and then hung right)
The horse in question finished the race beaten 103 lengths and was listed as dead three weeks after. I think when a horse shows signs of pain or fatigue it might hang to it’s right/left while trying to minimize the pain.