How ever the affair has been exposed, whether by discovery by the BS or confession from the WS, there must be proper closure to the affair. An agreement must be set up between the BS and WS that all contact with the OP must end and it must be permanent. The WS is in no position to bargain or make deals with their partner and try to keep the OP somehow active in their life. The WS must commit to the No Contact agreement and confide in their partner if the agreement is broken or if the OP has contacted them.
Writing a No Contact letter to the OP is the best way to end the affair. The WS is the one that writes it to the OP. There really is no format to it, except that it should be written by free will by the unfaithful partner. This isn't a "goodbye lover" letter...but rather should consist of stating that you are committed back to your relationship, that the A is over for good and there will never be contact again between them. It should be short and to the point, and the WS should state how selfish the affair was and how it caused tremendous pain to the BS.
Now, of course this won't be taken seriously by the OP if the unfaithful partner has had continued contact...this is a serious step towards reconciliation and it should be treated as such.
I would also let the WS know that you'll be reading the letter prior to him/her mailing it...there should be no hidden messages or hints that the WS will miss the OP. A letter is probably the best way to get closure for everyone involved...if you have your WS email or phone the OP...it opens it back up for the OP to respond...and that's what you are clearly trying to avoid.
In my case, I did not write a No Contact letter to the OM…we ended it on the phone. I did however write an apology letter to his wife, I never mailed it, instead she called me and I apologized profusely to her over the phone. I did however; write a No Contact letter to my best friend of 22 years. She was involved in several affairs and refused to end them and confess to her husband. Mangled and I both felt that if we were going to truly start over and have all deceit out of our lives, than she could not be involved in our relationship nor could our friendship continue. It pained me deeply to write her that letter…2 years later I'm still hurt by that. But I also know that it had to be dealt with in such a stern way, because she would have ended up hurting my marriage and possibly me again. And that was something I just wasn't willing to risk again.