I think what you're actually trying to ask is "How should an organization handle a slumping veteran?"
I think we can all agree that the answer isn't to demote them early on, like you suggested in the initial post that started this conversation.
I think you try what works. Each individual might handle things differently, and there might be unique problems and situations that led to the slump in the first place. I don't know the answers. I don't talk with the players. I'm not in the clubhouse. I'll leave that judgment call to those that are.
I'm not going to pretend to know what El Mole's deal is, but he's seemed frustrated to me ever since he arrived in Cleveland. Where's this guy:
I'm not going to speculate on anything, but based on what I've viewed of him, his demeanor at the plate, and now this sudden DFA, I just hope Franmil can get his career straightened out and get back to the happy, charismatic big slugger that I thought we were getting when we traded for him.