This is a question that the text provides no clear answer to. At no stage do Gregor or his family think of trying to discover a cure for his condition. This does present a rather worrying problem: does this in some way suggest an acceptance of Gregor's bug-like identity on both the parts of Gregor and of his family? In some ways, the answer could be yes. After all, Gregor, from the description that the reader is given of his life, already lives a bug-like existence even before he is transformed mysteriously. He has to work incredibly hard for little money in order to support his family and is not given any respect or status for the hard work that he does. In the same way, the speed with which his father and mother, and then his sister, turn against him, suggests a rather disturbing approach to Gregor that is confirmed when they start a newer and much happier life after Gregor dies. Note the final worrying sentence of the short story, when both parents look at their daughter and begin to think about finding her a husband:

And it was like a confirmation of their new dreams and good intentions that at the end of their ride the daughter was the first to get up, stretching her young body.

The emphasis on the "young body" of the daughter, and her youthful energy and exuberance which has only emerged after her brother's death suggests very strongly that the reason why the family did not bother looking for a cure is that they did not want Gregor to change back. They already treated Gregor as if he were a bug, and therefore, to a certain extent, the great big change was not actually that much of a change after all. The ease with which Gregor adapts to his new lifestyle likewise suggests the same: he thought of himself a bug.