Vivianna's husband abandoned her. His whereabouts are unknown.
A Lesson Before Dying
We learn in chapter 26 that Vivian's husaband is in Texas in a coversation between Vivian and Grant when Vivian's husband made contact about visiting rights of the children as a term of the divorce.
"I heard from him," she said. "He won't give me a divorce unless he can see his children every weekend."
My head started throbbing again. "When did you hear from him?"
"Yesterday, I was going to tell you today when I saw you"
"He's still in Texas?"
"And I suppose he had heard about us?"
"I suppose so."
Cited: Gaines, Ernest J. "26." A Lesson before Dying. New York: Alfred A. Knopf, 1993. 208. Print.