I have experienced this twice, unfortunately. In both instances, the congregation did what Jesus recommended in Matthew 18:15-17. First someone went to the pastor and warned him (in both instances the pastor was a man) that the adultery was known. Both times the pastor denied it. Then some of the members of the council followed up with another meeting. In both instances, there was no doubt of what was going on.
In the first instance, the pastor then repented, ended the affair, publicly resigned, reconciled with his wife, and is now serving in a different capacity at a different church. The woman also repented and reconciled with her husband, although they both left that church and joined another.
In the second instance, the pastor essentially said it was none of anyone else’s business, since the other woman was not a member of his church. It was then brought before the council (the supervisory body of the church), and it was decided to ask for his resignation. At that point, the pastor had begun the process of the extremely messy and unpleasant divorce, and we would need to have a special congregational meeting to fire him (or “withdraw his letter of call” I think it was). Rather than go thru that, he decided to resign. AIUI, he left the ministry altogether, divorced his wife, and subsequently married the other woman. I believe he now manages a small restaurant.
We are Lutherans, but as you might expect, the Catholic scandals of recent years have made all the denominations of the Church highly aware of inappropriate behavior, especially sexual behavior, of their clergy, and how it needs to be handled and not hushed up.
I have my issues with the ELCA, but I was very pleasantly surprised with how they assisted with the process. They were entirely fair-minded, not merely to the congregation, but to everyone else involved. They have not necessarily had a lot of practice, but this is not the first time they have had to deal with this kind of thing. They have all kinds of manuals that they shared with us.
It was bad, but it could have been worse.