How do you address a person who blames others (including God) for their sin?

Well, underneath that kind of response is a profound rejection of the biblical teaching on the sovereignty of God.

Now I would need to know those involved in order to know how to come at it, but, pastorally, I think I would say to the person,

"You know, if you say that God has betrayed you or that he didn't watch over you, or if you claim that God couldn't do anything about this, you're going to lose for your future the very thing you desperately need right now. You're in a crisis, whether some sickness or relational collapse (perhaps a divorce), and you've just thrown God away because he didn't keep you from it. What are you going to rest on? Now you may say, 'I don't want to rest on anything. I'll just make my own way.' But that's just devastating and suicidal."

So I would plead with them at the back end of a calamity and say,

"Now is the very time you need the sovereign God to help you get through this and to turn it all for good. But if you reject him at the front end by saying either that he is bad or that he is helpless, then you don't have a God who can, because of his goodness and resourcefulness, bring you through."

That would be one pastoral way.

And if I could speak with those who are influencing this person, I would take them aside and say,

"Look, before you say any more of what you've been saying, would you just help me understand what you do with all of these passages of Scripture that describe God as absolutely sovereign? What do you do with Daniel 2 and 4, where God raises up and puts down, and nothing comes to pass apart from his sovereign will. No man can say, 'What are you doing,' when he brings this or that."

So I would try to argue them away from giving this person that kind of counsel.