It's really not a management vs. Claude thing right now in terms of what the problem is. I'm not saying anything new here, but they go hand in hand.
Management gave Claude a good group of forwards and a ****ty defense. Claude decided, "You know what? I can still make this team defend well," and he makes his forwards defend starting in the offensive zone with third man high, constantly benches Ryan Spooner in favor of safer options like Schaller and Nash, and asks very little of his ****ty defensemen. And because he asks for very little, he gives heavy minutes to plugs like McQuaid and Kevan Miller who can only do the very little than Claude asks for.
Management looks at the situation and thinks, "Well, we have a good defense. And we gave Claude good forwards. So the offense should turn around." But that's not possible unless we play a more offensive, up and down the ice, style of play, which isn't happening under Claude. Or unless Claude gets more reliable defenseman that can allow the forwards to play more offense, which isn't happening under Sweeney.
I still think Claude should go, because even if a new coach isn't a guarantee to improve the product on the ice (far from it), we know that it's very unlikely that Claude coaches this roster to a high level and we don't know that a new coach and new system can't work. And we shouldn't be afraid of bottoming out. It's no worse than the 9 seed.
But in terms of assigning blame, it's not one or the other when it comes to Claude and management. Claude is coaching the team in a way that management forced him to and it's just not working.