Someone who worked at the same council at me did that. It was in the days before mobiles, so a lot easier.
He applied for a job in the LA where his bit on the side worked and got it. His wife was delighted he'd got a significant promotion and sort of enabled it by saying she didn't want to move, or the kids to change schools as they were just starting GCSEs/A-levels. He lived with his mistress Mon-Fri and his wife at weekends. He'd sometimes spend all weekend with the bit on the side, citing weekend conferences etc. It went on for 2 years.
I never knew how his wife found out, but she rocked up at his office one day to "surprise him". The teenage kids were old enough to leave by then, and she found digs for him and stayed there with him during the week. She actually used to come to work with him and just sort of hang around, drove him to meetings and so on.
Three months later, he took early retirement and was never heard of again. Neither was his mistress, who went on sick leave and never came back.
We were all gobsmacked, he seemed like such a nice, genuine bloke, a sort of absent-minded professor type, and very highly regarded professionally. His wife confided in his secretary, who was the biggest gossip in the county, so the whole sordid story became common knowledge.
Men can be such duplicitous and cowardly bastards.