In the book Lyddie what happens to Lyddie and Charles' father?

When
opens, Mr. Worthen, Lyddie's father, has been away for two years. He left
the family because the prospects he had for making money on their farm had soured. The maple
trees he had on his land did not produce enough syrup to be profitable, and the potash he hoped
to sell had no buyers. He had invested in sheep, but wool prices were not high enough for him to
earn any significant money from them. He left to try to keep the family from having to go to the
"poor farm," a place that the township operated for people who could not support
themselves. Such places were not pleasant; residents had to work on the farm for their keep but
had to follow strict rules. It would feel like giving up your freedom to go to live there--and
it would provide no way for you to ever escape poverty. 

Lyddie's mother has
a different description of why her husband left. She tells the children, "Your father went
out searching for vain riches. He ain't never coming back." However, the mother's
explanation cannot be taken at face value. She is mentally ill: "The truth be told, Mama
had gone somewhat queer in the head after their father had left." 

Still, the fact that the family has not even received a letter from Mr. Worthen for the
two years he has been gone indicates that something serious has happened to prevent him from
doing so, or that he does not intend to return. When Lyddie meets Ezekial, she imagines that her
father may be, like the runaway slave, "totally dependent on the kindness of others for
everything." However, if that were the case, he might certainly be given paper and postage
by some kind person, just as Lyddie receives such help from Diana. Possibly he had gotten ill;
Lyddie gets extremely sick later in the book, and if she hadn't had Rachel to care for her, even
Mrs. Bedlow acknowledges that Lyddie would have died. While Lyddie is working at Cutler's
Tavern, she gives up her dream of her father ever coming home, but later she considers the
possibility that he left for their benefit and he may have been prevented from
returning.