To understand the relationship between the Raven's shadow and the speaker's soul, you need to make some connections with the whole poem. Famously, the raven says, "Nevermore" in answer to the speaker's questions. This not only frustrates the speaker and increases the tension between the two characters, but it could also be a foreshadowing of what will happen to the speaker's soul in the end. The quote from the last two lines are, "And my soul from out that shadow that lies floating on the floor;/Shall be lifted--nevermore." The speaker's soul seems to be hovering like a ghost, which implies that death has overtaken the soul and it will never recover. The Raven and the shadow are both black, which color is a symbol of death; the shadow and the soul are next to each other on the floor, and neither will ever leave again, so they seem to be doomed to spend eternity together in a lifeless existence. It doesn't say that the man physically dies, and for a person suffering from a mental illness he may feel like his soul will never lift again just like the bird will never leave the room.
The raven is a very important symbol in the Norse, Celtic, and Irish mythologies. For example, the Celtic crow goddesses Badb, Macha, and Nemain dominated the battlefield during war. It was believed that the sighting of crows or ravens before a battle was an ominous sign of eventual defeat. By extension, ravens symbolized prophetic heralds.
In Norse mythology, Odin had a pair of ravens (Hugin and Munin) which traversed the earth to discover the fates of men. The ravens often returned from their forays to share their newly acquired wisdom with Odin. As both birds embodied Odin's thoughts, they symbolized his capacity for divination. By extension, Poe's poem draws attention to the raven's prophetic nature.
At the end of the poem, the speaker affirms that the raven still sits on the bust of Pallas. Here, Pallas refers to Pallas Athena, the goddess of war and wisdom. In Greek mythology, Athena presided over the fields of battle, and she also assisted humans in their seemingly impossible quests. For example, Athena assisted Heracles in his twelve labors, and she was instrumental in Perseus' success in slaying the Gorgon.
The raven's wisdom is derived from its ability to foresee the speaker's future. Thus, the presence of its everlasting shadow signifies that the speaker's life will be one of eternal grief. In other words, abiding sorrow will forever cast its shadows over the speaker's soul. If we look at the raven from a mythological standpoint, it can also be argued that the raven's presence is one that sustains the speaker in his labor of love, one where he dedicates himself to eternal misery for the love of a beautiful woman.