Gregor has a complex and conflicted relationship with his family. When the story opens, we see that his family are dependent on his salary, and therefore he feels very anxious to live up to his responsibilities and not do anything to jeopardise his job. However, when he turns so inexplicably into a giant insect, he can no longer do this and feels shame and guilt that he can't help his family any longer.
Along with this, though, he also feels gratitude when his sister helps him out in his new, strange condition. She does her best to look after him, and his mother, too, still seems emotionally attached to him. It is a different matter with his father, however; evidently the relationship between the two has always been difficult. (This reflects Kafka's strained relationship with his own father.)
As time goes on, however, and Gregor becomes weaker and more immobile, the situation with his family also deteriorates, and he starts to feel neglected by them. As he remains trapped in his room, even his sister ends up wholly resenting him, seeing him no longer as her brother, but as a monstrous burden on all the family. Gregor, too, comes to accept this opinion, and eventually wills himself to die, feeling that it will be a relief both to himself and his family. He still feels enough affection for them that he wants to perform this last self-sacrifice for them:
He remembered his family with deep feelings of love. In this business, his own thought that he had to disappear, was, if anything, even more decisive than his sister's.
Certainly the family seem to experience a feeling of deep release after his death. This is the most troubling aspect of the story: the implication that the family are ultimately better off without Gregor.