Yes, I believe X has a responsibility to Y.
Although the girl has more responsibility to X, being cheated on is a humiliating experience, and nobody should cause that pain between two people.
There are times when people should restrain their own needs and wants, and this is one of them. The girl obviously isn't deeply attached to X (when in real love, there is only one), and if she were serious about Y she should leave her current partner for him.
IMO, if the girl doesn't have the strength of character this is where Y needs to make her choose before letting anything happen.
At the least I think it'd be important that X found out by some means, as even more humiliating than being cheated on is being cheated on and being the only one not to know about it. You find out eventually, and it'd crush anyone who believed they had something with their partner. I don't know if Y should do this, but in their shoes I'd be making sure the girl did.
Then again, cheating isn't something that agrees with me at all. I think the only except to that would be if the girl and Y were actually in love, something happened on the spur of the moment, and she left X straight away. But that doesn't sound like your hypothetical situation, lol.
=> Jess
edit: if Y doesn't know X exists though, he obviously isn't responsible for the situation (as he isn't even given the option of doing the right thing)
