Impact of self-published "failure" stories of corporations on prospects and customers

Most organizations publish their success stories in their marketing collateral. However, I wonder what if organizations were to publish their failure stories.

Will the stories generate empathy in the prospects? Will they provide a (more) human look to the organizations? Will prospects better identify with organizations?

Will the influence be different if the stories are published at different times?  (What if the organization were to acknowledge and publish their mistakes during economic recession, or during its own tumultuous times?)

Will using a celebrity (who has failed, and later risen through the ranks) to communicate the failure stories make a deeper impact?

Will the answers to these Qs differ if the organization is non-profit? Does the concept apply in B2B marketing?