Nothing it is not my business to be involved in that part of their relationship and I still love both my parents. Why hurt the other one now?

Actually, I had heard my parents argue about my father cheating on my mother. My mother was just jealous and she couldn't have a solid proof for it. I thought, if I'd found out that my father was really cheating when he was alive then I can do nothing about it. They're my parents so I still respect and love them. But, if my family were broken (like what others have experienced) and my other parent lived in misery and died because of that then I don't think I could forgive the cheater.

If your parent is already dead, then there is nothing you can do. I might feel angry, but then so what? they're gone. All mistakes should be forgiven and forgotten. After all, all we have is their memory. Our parents are not perfect and they do sometimes make grievous mistake. Some people expect their parents to be perfect and they will be very angry and dissapointed to find out that it's not true. One thing for certain is that I will never tell the other parent who is still alive because I don't want to upset him or her further. We just have to let go.

I've never been in this situation. I imagine it would be hard to deal with the conflicting emotions it brought up.
My actions would depend on how I heard about the mistake. If my living parent didn't know about it, I would keep quiet and struggle with the emotions it brought up on my own. If I was told by my living parent, I would listen and offer support, not judgement.
In any case, I hope I wouldn't judge. People are who people are. Even Mom and Dad.

I might be a little upset to hear that one of my parents would have actually done that to the other, but, if they are already gone, it doesn't really matter anymore. No good can come be being angry with them. It would just be water under the bridge. Besides, like you say, it was probably none of my business anyway. :-)

Well, given that the parent would already be dead, I could not “do” too much on his/her part, except to accept the fact of what happened (if it truly bothered me) and try to help the other parent cope with this information (if he/she were truly upset over finding out about the cheating). I am not sure I would spend my life being mad at my dead parent, however. I would not want a single (or even multiple) acts of indiscretion to ruin the memory I have of my parent. Preserving mostly happy memories is key in a case where you are already grieving and trying to cope with the death of a loved one. You might feel upset over his/her death already and so blaming him/her for cheating and being mad could be one way to deal more easily, since you could make an excuse for letting yourself feel less pain (“he was a bad person anyway having done that to my mom, so I won’t feel sad anymore…”). This is not what a healthy grieving process is about, however, and eventually if you don’t deal with all your feelings effectively and have closure, the death will take a grip on your life and you won’t be able to make peace with his/her death. I have not lost a parent yet, Thank God, but I did lose both grandparents a few years ago within a 5 month time span. I think if I found out today that either of them cheated on the other during their marriage, I would be more surprised than mad. They might have had their reasons for cheating or they might have acted in total self-interest. But really, it was likely a long time ago and quite frankly is not any of my business. With parents, I think that unless the cheating or an affair would have severely, negatively affected me or my siblings during their marriage and I still felt the after-effects from it (maybe constant arguing by my parents or the cheating parent was never home), then I might be a bit resentful over their choices in life. But once again, you cannot change the past. Especially not that of a dead person.

I would stay out of it. It is their business and I don't know all the facts of the situation. Maybe the marriage was over before the cheating incident or maybe they had an open relationship of some sort and they both had cheated. There could be any number of reasons and it wouldn't be right to judge when you don't the whole story or only one side of the story.