There is no clear remark or statement that indicates what actually was done to care for Tom Robinson's children after he is arrested and after the trial. However, there are some things that characters have said that suggest that the children will be looked after. For instance, when Scout and Jem accompany Calpurnia to her church, when the Reverend Sykes addresses the congregation he tells them,
"You all know Brother Tom Robinson's trouble. He has been a faithful member of First Purchase since he was a boy."
That Tom has been a good person throughout his life is also established with Scout's observation in Chapter 19 after she listens to Mayella's testimony,
Tom Robinson was probably the only person who was ever decent to her.
Tom himself testifies that he did not want to ever harm Mayella, even when she gets too close and hugs him,
"Mr. Finch, I tried. I tried to 'thout bein' ugly to her. I didn't wanta be ugly, I didn't wanta push her or nothin'."
With her husband gone, Helen Robinson and her children undergo hardship; however, Link Deas hires Helen as his cook so that she can provide for her family. In Chapter 27, Scout narrates that she "never knew who took care of her children"; however, the reader can safely assume that the church members will look out for these children because they understand the need, and because Rev. Sykes will see to it that the children are looked after.