Now, with thanks to EW, it seems that John Goodman has at least partially answered that question. Goodman conducted an interview with The Sunday Times (behind a paywall) in which he commented that his character Dan Conner will "be mopey and sad because his wife's dead".
There's no official word from ABC at time of writing. Ironically, Dan himself was revealed to have died in the original series finale back in 1997 - a move that was retconned for the series revival this year.
Despite the controversy, Goodman seems to have remained somewhat loyal to Barr herself - firmly stating that "she's not a racist" and that he was "surprised" by the response to her tweet. He also reveals that he emailed her to thank her for relinquishing her rights to the series to allow The Conners to move forward, but that he hasn't received a reply.
The Conners will premiere on October 16, 8pm ET on ABC. Matt Davidson is a freelance writer for IGN. He's available on Twitter if that floats your boat.