The Metamorphosis is a study of the complex interplay between family and individual responsibility. Gregor, for example, believes that it is his individual responsibility to help out his family. His parents have a debt that can be repaid if he works for a particular firm in a job that he loathes as a traveling salesman. However, he figures that he can leave the job in "another five or six years."
Likewise, the father at least pays surface-level family responsibility after he throws the apple at Gregor that lodges in his carapace and makes him sick. The father decides
as a family, there was a duty to swallow any revulsion for him and to be patient, just to be patient.
However, family patience and responsibility to Gregor wears out quickly when it becomes obvious that he is nothing but an unsightly, repulsive burden to the family. He adds to their work load and contributes nothing. Soon the family's true, less than idealistic, colors emerge. The true feelings of the family are that individuals need to take responsibility for themselves and not become a long-term burden.
Gregor's feelings seem to be more complicated. He is willing to take on a burden and sacrifice himself to help his parents out, but it is not clear that he is entirely altruistic: the debt may be an excuse for him not to make changes in his life. When change does come, Gregor feels some relief that he can be alleviated of his responsibilities and "rest." At the same time, he also accepts that he has become such a "torture," as his sister puts it, that he must die:
If it was possible, he felt that he must go away [die] even more strongly than his sister.
This is a family where beyond a certain point, every person is responsible for themselves and pulling their own weight and where Gregor's death is a relief.