Regarding Shadow Dragons, the Monster Manual (p. 85) states:
Any damage-dealing breath weapon possessed by the dragon deals necrotic damage instead of its original damage type. A humanoid reduced to 0 hit points by this damage dies, and an undead shadow rises from its corpse and acts immediately after the dragon in the initiative count. The shadow is under the dragon's control.
Does this necessarily mean that the humanoid becomes the undead shadow? It should clearly state that, if that is the case. This matters in case the party wishes to raise the character from the dead via a revivify or raise dead spell.