This was tested in single player
Used NBT edit to reduce max player health base to 10 (5 hearts) and armor display drops down behind remaining heart display.
Had reduced player health on map, player dies, the max base health is returned to 20(10 hearts).
The armor display issue with less than 5 health has been fixed in 13w25a snapshot but the Max Health reset on death is still present thought it's more likely linked to this report now, MC-17876.