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I think that they simply begin enjoying better lives after Gregor becomes a big insect. His father gets a job and has more purpose in life. The daughter's youth is mentioned more and more,
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.
Gregor became old news and his family felt his sacrifice was preordained to allow them a better life.