re: Is it possible for any relationship to stay intact after cheating?

It can but it often depends on how long the affair went on and how it was discovered.

If it was a one-night stand type, and the cheater immediately confesses and gets help, then there is a good chance the relationship can be repaired.

But if it was a long, drawn out affair with many cover-ups and multiple meetings, and the cheater is busted by the other spouse or someone who threatens to expose it, now it becomes harder (though not impossible).