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These situations suck!
Input costs are meaningless and the current value of the business is the only thing that matters. Total the assets and offer market value for their half if they're willing to release the brand/logo/identity in exchange for you taking over the lease. If they decline, make it clear the doors are shutting and they can either buy you out or everything will be liquidated.
If the business model is sound, take what you've learned and go at it alone with a new and improved brand/logo/identity.
I actually had them counter with the offer I made them. 6 months later I had a much better logo/identity up and running and they folded up shop knowing they ****ed up. I didn't really know it at the time, but getting the chance to start fresh with my own image of the brand was what I should have pushed for in the beginning.
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