I now have a new definition for remnant:

Remnant

Noun

Concentrated energy; the leftover residue of a soul inhabiting a normally inanimate object.

Why: A soul is literally energy manipulated to take the form of a former living being. When a soul is inhabiting an inanimate object, the soul is in a half dormant stage, so the energy residing within has nowhere to go, and can't stay there without utterly destroying the area with a mile, because the energy is so intense. And, since energy cannot be destroyed, it dilates itself into a less dangerous form, or remnant. When a living being consumes this energy, wounds heal faster, and the body becomes younger. (That would mean that William is immortal to time, but not to the blade or poison)

Where does this energy come from?

It comes from the intense emotions the souls experienced while they died. Since certain emotions ignite the body chemical known as adrenaline, or, energy, and that energy cannot be destroyed, it makes up the vast amount of energy that forms a soul. Some emotions, such as fear, are slightly weaker than when it comes to Fury, or Agony. Those two emotions would definitely spark a large amount of adrenaline, and soon, energy.

(Part 2 will come soon, covering the concentration of energy, the extraction of Remnant, and a scale on which emotions that have the most energy.)