I don't think it will go as far as a Chapter 7, at least not yet. They may convert from 11 to 7 at some point in the process, but that's if the court determines that their ability to sustain itself as a going concern is challenged.
It's most likely going to be a Chapter 11. The only time the topic of Chapter 7 came up was when BoA, JPMorganChase and Citigroup mentioned to the media that they are pushing for Chapter 7 as they want to recover their debts expediently. Under Chapter 11, it's a slower process. I'm not excusing Sears or Eddie Lampert by any means but banks are greedy. They don't care if a business lives or dies, they just want their money and fast.