Another interesting thing to read for is to look for details of description of the apartment. As it turns out, there are several doors to Gregor's room, not just the one that leads out to the main living room. Gregor's room seems to be a central room in the apartment, and the other bedrooms also have access to this room, though no one would dare enter the room now. Gregor is literally central to their lives, yet closed off by doors that are perpetually closed against him.
Doors are funny things. They are a transformation from one world to another. This is not literal normally, but Kafka plays around with it. The door is a standard symbol of change in literature. When you go through a door you are going over a threshold to something else.
Gregor is not only an embarrassment to his family, he actually disgusts them...
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and eventually makes them angry. The door is their attempt at separating themselves from the unwanted creature who was once their son. It is helpful to note that his family felt this way to some degree even before his transformation; Gregor was nothing but a paycheck to them. On the other hand, the door is a protection for Gregor. It shields him, most of the time, from the ugliness, anger, and hostile curiosity of whoever is on the other side of the door. Thetragedy, of course, is that these negative emotions emanate from his family, the people who should be most supportive of him. The presence of the door ensures his privacy; it also ensures he can be neglected by those who should take care of him.
What it shows is that their relationship is not at all tight nor deep deep, and, how could it be? Poor Gregor's life is so focused on work and on his consistent routine that it renders him unable to establish any true and meaningful human connections. This shows how Kafka intends to present the superficiality of society: By giving us a very complex, fantastic, and nonsensical situation spoken under the perspective of characters who are unable to think something other than life as he knows it. In addition to the shallow ties of the family, we also learn about the obliviousness with which the family takes Gregor's changes.
They basically focus on the tediousness of the situation rather than on Gregor's well-being. Like the previous post noted, they literally shut the door on Gregor. They established a clear difference between them and Gregor. The family made sure that they were in no way connected to him emotionally, psychologically, or even as a family. Even Gregor, himself, had a massive disconnect between himself and his situation. The door is the symbol of that family divide. Gregor will exist and cease to exist in his own little world in the bedroom. Meanwhile, life goes on as usual for the family, separated from Gregor.
Well done for noticing this! Yes, it is clear that the way that Gregor is "shut away" into his own room and how, at first, only his sister will enter, and then, not even her, says something very profound about Gregor's standing in the family. Their natural instinct upon discovering the true nature of Gregor's transformation is to lock him away and keep him separate and isolated from themselves. We are told that his parents in particular cannot even bring themselves to enter his room during the first two weeks:
During the first two weeks, the parents could not get themselves to come into his room, and he often heard them expressing their great appreciation of the sister's efforts...
Of course, the way in which Gregor is shut out from their world and the violence with which any trangressions of this boundary are met, such as when his father bombards him with apples, symbolises the way that Gregor is treated as an unwanted outcast, a figure that his family do the best they can to ignore and pretend does not even exist. The real question we have to ask ourselves though is whether this was the case before Gregor's metamorphosis.