Closure is this mythical thing where both parties in a relationship (adulterous or otherwise) have a mutual conversation where they agree to end their relationship, agree that it was fun whilst it lasted but that, for whatever reason, it now has to finish. Both parties go off into the sunset happy that they have finished it on an equal footing.
REAL closure IMHO and IME is when a person admits to themself that their (adulterous or otherwise) relationship is wrong for THEM and for the people that they love, and that it needs to end.
Speaking as an ex-OW, and trying to see this from your DWs POV I think that part of her continuing to text John is because SHE hasn't made the choice to end it - your discovery of her sexting did that. It's like dieting or giving up smoking - people can tell you that it's bad to smoke or to be overweight but you have to WANT to give up smoking/eat more healthily.
I'm not condoning AT ALL what she is doing, but I have walked a mile in her shoes and can see where she is coming from. The problem is that she has to WANT to stop, and your hurt and anger is not having any effect on her.
I think her problem is as much a lack of respect for herself as it is for you, even though from what you have posted it seems otherwise. I know what it feels like to hate yourself so much that you will put at risk and push away the people that love you most. I'm putting this as a counter argument to the 'lack of respect for you' argument but am not sure where I'm going with it!