One way to look at Gregor's transformation into an insect is that it is symbolic of an event in his life that keeps him from being able to work to support the family. He suddenly goes from being the main breadwinner to being someone that they have to pay for. In the book, Gregor becomes the epitome of uselessness by turning into a large insect, one thing that we have almost never found a use for. His inability to work is just further worsened by his family's obvious repulsion to him, even though he can't see it. This is symbolic of the family being in some way disappointed in him that he failed to continue working to support the family.
As the family gets more used to Gregor not being able to work, if he thinks he's at fault and his family doesn't disagree, Gregor might distance himself and close himself up in his room, where he will work more at his desk, which we see mentioned in the book several times. Also, the rest of the family might carry in family affairs without him. This is all symbolized in the book with the fact that Gregor listens to their conversations about finances through the door of his room.
However, this starts to break apart whenever Gregor is beginning to be put off to the side and actually dies. The removing of the furniture could be symbolizing his leaving their house, but coming back occasionally, which throws off the game of the rest of the family. His death and what happens afterward symbolizes Gregor being ultimately cast out entirely by the family, and they just continue their lives as if he had never been there.
