I'd agree that telling -- and the betrayed spouse's response ought to be based on the relationship between them; but I can't agree that it's necessary to tell after the death of the cheating spouse. Since you've never lost a spouse, you really have no idea how far the bottom drops out of your life. Having someone pull one more plank out from under you is no favor.

It should be the cheater's responsibility to tell on him or herself, not the other party. The cheater is the one who broke their marriage vows. On the other hand, a "friend" no matter how close, who would try to seduce my husband would no longer be my friend, period.