Soul is an abstract matter that composes all conscious beings in the Underground.
Inside the Soul
Humans, Players, Reapers, and Noise are all made of this Soul. The form that any mass of Soul takes is determined by the code it is bound to. By breaking up a being into a Soul and rebinding it into something else, a being can be transformed into something else, even into a pin, as was the case with Rhyme. This is also why high ranked Reapers have a Noise form, as they possibly have the ability to change themselves from Noise, back to Reaper and back to Noise again.
While many would think that Erasure is the complete destruction of one's Soul, or at least a majority of it, Erasure is simply the breaking down of an Underground being into their Soul. It is possible for anyone to Erase another for this reason, although you need to be strong enough to do it. After a being is erased, all of its Soul remains in the Underground until rebinding.
It is unknown though if Souls ever disappear, although high rank Reaper haven't attempted to "revive" people of the past. The reason behind this may pertain to a rule created by the Angels which is against the rebinding of a "defeated" Soul.
Power over the Soul
Anyone would understand that each person has a different amount of power over the Soul. Everyone is able to unbind a Soul, provided they have the tools and strength to do so. But, just like how it's not possible for everyone to be skilled enough to make something, not everyone is able to rebind a Soul back into existence.
Humans/Denizens of the RG
Living humans have a stronger "binding" than Souls that have died. Rather, once a Soul is unbound once through death, the binding becomes loose and requires tremendous power to be bound back again to such strong levels. Because of this strong binding, the Soul of the living requires death in order for their Soul to transfer into the UG. And as with all humans, they have no power over "rebinding", as they are both unaware of the UG and not capable of such kinds of resurrection. They also can't Erase Souls of the UG because they are unaware of the UG.
Aside from the strong binding, humans may also be producers of Souls, as Noise come from the negative emotions of the living people of the RG.
Players are just players; they've been brought into a game so that they can exist in the RG again. They possibly have the minimal amount of power over the Soul, as they lack the knowledge about Souls to do so. As stated before, anyone can unbind a Soul through Erasure, which players can do.
A being's Soul also determines the type and power of their Imagination, which is the force in every person that powers pins. Using psychs thus refines the Soul of the user.
Reapers can manipulate Souls to create Noise from pins. And the stronger a Reaper is, the more they can manipulate the Soul itself. If one is the Composer especially, they can rebind the soul back into the existence of the RG.
Because Reapers are Players who have "ascended" to a stronger or more promoted state, the abilities Reapers wield are also based on the type and power of their Imagination. Even so, Reapers are usually strong as they had to have survived at least one week of the Reaper's game.
Noise also consume Soul from the people they possess in the RG, stealing part of their Soul and causing a rush of negative emotion. Some Noise are created directly from these Souls on certain occasions. This is why people of the RG experience rushes of euphoria after being liberated from Noise.