While Gregor narrates almost all of the story, a great deal of his narration in the second and third parts is actually just describing what his family is doing. He talks about their conversations that he listens to during dinner, the new people that come into the house, and how the members of his family are each progressing in their personal lives and work. While his feelings do change over the novel, his general personality remains basically the same. Throughout the book, he clearly wants to be a part of and help his family, and he wants to make things as easy as he can for them. And, though his worsening treatment makes him angry, he still holds these basic desires and has a positive attitude towards his family. His physical change far exceeds his mental change, and change in character is one of the main criteria for a protagonist.
Gregor's family, on the other hand, have a complete change in character from the start of the novel to the end. When Gregor is first transformed, they seem to be sort of lazy and generally unhelpful with making money and with supporting the family; that's Gregor's responsibility. However, Gregor is taken away from them, and they find themselves without a source of income. In this situation, both of Gregor's parents and his sister are able to step up and get jobs to save the family. As the novel progresses, we see the three of them start to move away from Gregor; he's rather forgotten and his feeding and cleaning are seen as quick, routine chores.
Seen in this light, The Metamorphosis could be a completely different story. A family has to deal with (what amounts to, for the family) the death of their son. They are able to slowly move on from him, and support each other as they try to start a new life. At the end of the book, it could be said that all three of them are in better positions than when they started the book; all have employment and are doing something with their life, and there's indication that they'll be able to be happy. It's possible that Gregor, with his complete dedication to and pride in being the family's sole source of income, was actually in a way holding the rest of the family back.
Gregor holding the family back is a common theme throughout the book, as the presence of the bug that's the last remains of him disturbs the family and somewhat prevents them from moving forward. This is shown by his sister's speech at the end, where she says that the family has to "get rid of the idea that [the insect] is Gregor," and that the animal "plagues" them. The family dissociating the insect with Gregor's memory coincides with the bug's death the same night, which brings up the possibility that the insect in itself represented the family's reliance on Gregor; it got weaker and weaker as the others got jobs and started supporting themselves, and it finally dies when they leave the apartment that Gregor bought them and go to start a new, independent life somewhere else.
